Among all the dispute and conjecture that has surrounded the life of JD Salinger, one mystery remains especially puzzling. What did he produce after ceasing to publish his writing in 1965, and will it ever be read? It seemed possible that more work would come to light after Salinger’s death in 2010. In 2013 a documentary and accompanying book claimed, among other things, to describe the contents of five new Salinger books that would be forthcoming by 2020 at the latest, yet here we are at his centenary and there has been no sign.

I ask Salinger’s son Matt about the rumours of new material when we meet for breakfast near his home in Connecticut, and he doesn’t mince words. “They’re total trash,” he says. “The specific bullet-point dramatic quote-unquote reveals that have been made are utter bullshit. They have little to no bearing on reality.” He has been reluctant, until now, to talk about his father at all. “I’ve gotten away with not having this kind of conversation for 58 years,” he says. Still, he is ready, now, to confirm that other writing does exist. His father “teemed with ideas and thoughts, and he’d be driving the car and he’d pull over to write something and laugh to himself – sometimes he’d read it to me, sometimes he wouldn’t – and next to every chair he had a notebook.” He assures me that “most all of what he wrote will at some point be shared with the people that love reading his stuff”. When I ask why that moment hasn’t yet arrived, he is disarmingly direct. “It’s not ready. He wanted me to pull it together, and because of the scope of the job, he knew it would take a long time. This was somebody who was writing for 50 years without publishing, so that’s a lot of material. So there’s not a reluctance or a protectiveness: when it’s ready, we’re going to share it.”

‘Funny as hell’ … JD Salinger in 1950. Photograph: Gado Images/Alamy Stock Photo

Tall and striking, with an air of warmth and amusement that belies his evident doubts about talking to me at all, Matt Salinger is an actor – probably best known for playing Captain America in the 1990 film – and a producer of movies and theatre, most notably Pamela Gien’s The Syringa Tree, which he “put my whole self into for a decade”, producing an international hit. What becomes clear is that he has been immersed in his father’s material for years – pages typed on Underwood and Royal typewriters, as well as what Salinger called “his squibs, or his fragments” on ordinary paper cut into eighths: “a lot of handwritten, very small notes”. When he began work in 2011, Matt never expected it would take eight years. He feels “fortunate”, he says. “Reading this stuff for the first time” has been “an emotional thing”, like having an ongoing dialogue with his father. “A lot of my friends at this age, their parents are dying or have died and they’re just gone, you know. And my father’s not gone. He hasn’t died for me.” Often he will “just have to stop what I am doing”, struck by something “that I recognise that for the right reader, whether it’s millions or hundreds of thousands or tens of thousands or three or one, it could just be the one right reader that needs to read that. I feel the pressure to get this done, more than he did.”

When I ask how much longer it will take, Matt replies: “We’re definitely talking years,” though, he hopes, fewer than 10. “When his widow and I were first gauging what needed to be done after he died, I knew that I wouldn’t be producing any films or theatre for a while and I knew that I would only be doing enough acting to keep my family’s health insurance.” Often people will approach Matt in public, at a ski resort or bike repair shop – “it’s always my credit card that does me in!” – with “a cri de coeur”, pleading to know if or when more work will appear. One older woman said she didn’t want to die without having read what more there is. “If that’s not pressure …” he says. “I don’t take any of this lightly.” He adds, “I don’t owe an apology, I don’t think, but your readers should know that we’re going as fast as we freaking can.”

We’re never going to be merchandising anything. There’s never going to be a Salinger vodka

Of the rumours that have spread, Matt laughs that “anyone that understood my father at all would find the idea hysterically funny that he would write a book about his first brief marriage. It’s so far beyond the realm of plausibility.” He’s unwilling, at this point, to reveal anything specific, though it’s clear that there will be more about the Glass family, who inhabit many of his best published stories. He says there’s “no linear evolution” in the later work: “It becomes clear that he was after different game.” Matt believes the new work “will definitely disappoint people that he wouldn’t care about, but for real readers … I think it will be tremendously well received by those people and they will be affected in the way every reader hopes to be affected when they open a book. Not changed, necessarily, but something rubs off that can lead to change.”

Matt was born in 1960 and immortalised a year later in the dedication to Franny and Zooey (Salinger writes that he offered the book up to the New Yorker’s editor, William Shawn, “as nearly as possible in the spirit of Matthew Salinger, age one, urging a luncheon companion to accept a cool lima bean”). By the time Matt came along, the second child of his father’s second marriage, in 1955, to Claire Douglas, Salinger had already published most of the work on which his monumental reputation rests. After the perennial bestseller The Catcher in the Rye (1951) came For Esmé – with Love and Squalor, Franny and Zooey, Raise High the Roof Beam, Carpenters (the last three mostly consist of stories that appeared in the New Yorker from the late 1940s to 1950s), and then that final New Yorker story, “Hapworth 16, 1924,” in June 1965.

As a child, Matt didn’t hear much about his father’s work. “We were more likely to talk about the Dartmouth football team, or what are we going to do when I pick you up on Wednesday.” He speaks of the respect his father had for children: “He did see the world as something that will just work on fucking you up, if allowed to. He had a real belief and even reverence for the innate intelligence and beauty of kids before they’re homogenised.” Matt’s sister, Margaret, who is four years older than him, offered in her 2000 memoir Dream Catcher a much darker portrait of their parents and childhood, which Matt refuted in print as “gothic tales”. (These days he keeps her informed about plans for the centenary and says: “I only wish her happiness.”) JD Salinger’s first marriage, to a German woman just after the second world war, lasted less than a year. After his divorce from Matt and Margaret’s mother in the 1960s, he eventually married Colleen O’Neill, who now has joint charge of his literary trust with Matt.

That means being on the first line of defence, “fighting lawsuits and tilting at windmills”, fending off what Salinger called “wanters” (I can’t quite tell if the “relentless” Harvey Weinstein, who was “after me forever” to get a film of Catcher off the ground, counts as one of these), and hindering, for instance, the republication of several early stories that Salinger did not want collected. (His father’s feeling about those stories, which were “youthful exercises, part of his process, his development as an artist,” seemed to Matt to be akin to “when you’re having a bad night and you’re trying to go to sleep and you think of things and you just have that wince, ‘Did I really say that?’ or ‘Did I really do that?’ …. There was also more ego in those, he called himself a showoff when he was young.”) Matt has been “keeping up that vigilance. And it’s not a sporting exercise, I don’t do it lightly, it’s no fun. I do it because my father would have done it and out of love for him, and out of love and protectiveness for his work and his books.” He has made himself an expert in international copyright law, and speaks with energy about “European countries where their law came more from Hegel than from Locke.” In the cottage industry of Salinger quasi-biography, he identifies a “weird sort of inverse relationship,” in which “the better somebody knew my father, the less likely they were going to be to talk to anybody. And there was really no middle ground, you either knew him really well and intimately or you just knew him completely casually.” He himself is painstakingly precise in what he says about his father or the work, often second-guessing a word or phrase, reiterating that his father would probably hate what he’s saying and how he’s saying it, or deciding, mid-way through a seemingly harmless sentence, not to finish it. All Salinger’s files, which in his lifetime were kept in a pair of safes in his house – “and thank God they were”, Matt remembers, because otherwise everything would have been lost when Salinger’s house burned down during the 1990s – are now in a high-security storage facility.

His work was everything to him ... the rest is just noise and mythologising and pathologising

Salinger’s desire for privacy, of course, only increased the feverish interest of the press, and his son kept track of the shift in words habitually used to describe him as the decades passed, “seeing when the word recluse started being used. And then that morphed in the common vernacular among journalists to ‘famous recluse’, and then it became ‘infamous recluse’. In the last 10 years, it became ‘notorious recluse’, and if you really think about that word, it’s damning, it has all kinds of psychological overtones, and it’s dishonest, and like so much that’s written, it says more about the person who’s writing it than it does about the subject.” There was nothing sinister or mysterious, Matt insists, in his father’s wish to live and write in private. “He just decided that the best thing for his writing was not to have a lot of interactions with people, literary types in particular. He didn’t want to be playing in those poker games, he wanted to, as he would encourage every would-be writer to do, you know, stew in your own juices.” Salinger gives a vivid, impromptu impression of his father, on the phone, clearing his throat: “Sorry Matt, God, I haven’t used my voice in three days.” Time alone was simply “what he needed for his work, and his work was everything to him”. The rest, Matt says, “is just noise and mythologising and pathologising and people’s own neurosis”.

At one point he shows me a copy of one of the small, handwritten notes that he came across recently, as “an offering or a gesture” to Salinger’s readers. “Anyone that loved his writing and thinks they cared for him in a certain way might have been alarmed or concerned at so much of what’s been written,” he thinks, and he wants them to get “a glimpse” at how Salinger was feeling late in life. The piece, “like a haiku in a way”, describes a moment of unexpected and “still, not disquieting” happiness while resting, having been up working at the typewriter since six that morning: “and, through the window by the bed he saw that snow was falling without rush but copiously into the grayness, the December unsunniness of the late afternoon, and it was suddenly, bliss, sheer bliss, to be alive and watching and about to fall asleep, nearing sleep. Bliss. Thank you, God!”

He is currently deciding what should be included in an exhibition at the New York Public Library in October – “talk about things that go against my nature!” – that will have some manuscripts, photographs, objects, letters. But, he promises: “We’re never going to be merchandising anything. There’s never going to be a Salinger vodka.” Going through some of the hundred or so letters his father wrote him, “often funny as hell”, dating from the early 1970s to 2009, he offers to read some to me. A letter from 1976 links an interpretation of Shakespeare’s Julius Caesar with the TV journalist Dan Rather’s soppy coverage of Nixon’s resignation and with a tennis match between Chris Evert and Evonne Goolagong, whom he sees as “like some Star Trek girl from outer space ... Too peace-loving, too placid to be effective against any of the hustlers from Earth.” He writes:

“There’s probably no limit to the extremes of infantile and Zoo-like behavior adults will take to, or revert to, if they’re in a group (which means any number of people in excess of two – and on some occasions two’s a mob, especially if there’s booze around), and if the organised shit-throwing is given the permissive, O.K. general heading of Fun & Games, or if it’s vaguely categorized as Letting Off a Little Steam Once in a While Never Hurt Anybody, Mac. Oh, groups at large give me the willies, Da. Group enthusiasm, of any kind, either for cheering or lynching, makes me very uneasy …”

Elsewhere he expresses delight in catching one of Matt’s appearances on TV (he praised his honesty and brilliance, “right in the middle of all that SHIT!!”). Other letters are very emotionally direct. Going through “all those old papers and letters yesterday made me all the more aware how happy and relieved I am to be living in the present, not the past. I can’t say I cared much for the War or military school or my childhood. These Cornish years with you and Peggy and this house and you and the fields and my notebooks and work and you and Lili and Schotland and Nice Doggie and Rosie and you and Sri. R. and the Nuremberg Egg and our trips to London and Lake Placid and Dublin and Montreal and Andover – these years have been what I would call my real life.”

The preparation of his father’s writing is, Matt feels, the most meaningful work he could be doing. “You’re only given one life. Most of the movies that I produced were crap.” He also assures readers that “when my father said that everything he has to say is in his fiction, believe it – it’s there. I think when more of his writing is made accessible, he covers everything that the discerning reader would care about. My job is to help that happen as soon as it can, and stay out of the way.” He adds: “Whatever I have to offer up on his behalf, I’ll certainly do with more belief and faith and love than I offered that lima bean to whoever it was. And hope.”