Glenn Close picks up the phone in her Montana home and all hell breaks loose. Between waves of helpless laughter, she tries to explain exactly what is causing the chaos. “Sorry to be – can you hear me? – oh my God –there’s a dog going past the house and – wait there.” The pooch making all that racket is Pip, Close’s pet havanese. He only recently watched one of her films, she tells me; fittingly enough, it was the live-action version of 101 Dalmatians, in which she is a regally evil and blazingly camp Cruella de Vil in black-and-white fright wig and taloned gloves. “He was absolutely glued to the screen,” she says. Possibly in terror at her puppy-killing plans. Pip has his own Instagram account (he’s Sir Pippin of Beanfield). “Everyone knows about him, so I’ll have to start posting more things on there,” she says.

Now may not be the time. Over the next five weeks, the 71-year-old actor will have numerous awards ceremonies to attend – including the Baftas on 10 February and the Academy Awards a fortnight later – and in all likelihood more statuettes to collect in honour of her performance in The Wife as Joan Castleman, the overlooked spouse of a Nobel-winning novelist, played by Jonathan Pryce. Since its premiere nearly 18 months ago, the film has been seducing audiences and critics everywhere, with the Oscar buzz for Close building to a deafening volume. A few weeks ago, she won a Golden Globe; her pop-eyed, gobsmacked expression when her name was read out, followed by an eloquent speech in which she paid tribute to her late mother (“who really sublimated herself to my father her whole life”) and urged women “to find personal fulfilment”, has won her new legions of fans.

Watch Glenn Close’s acceptance speech at the 2019 Golden Globes

“I’ve been floored by the response,” she says. “People are coming up to me in airports to talk about my speech. It’s almost like I don’t know what I’ll say if I win again. It’ll be hard to top. It was such a spontaneous moment for me, and that kind of thing you can’t really repeat.” Close, who has been married three times, denies that her mother was a direct inspiration for her portrayal of Joan. “I didn’t channel her. Although of course I had seen her taking the back seat to my father my whole life, so it was in my DNA. I had a well of subliminal experience to draw on.” Her speech delivered the right sentiments at the right time. “It’s not that they hadn’t been expressed before, but I guess they resonate in this moment. For that whole generation, pre-feminism, that’s the way it was. That was the norm. It’s caused me to look back at my two grandmothers, who were basically unfulfilled women. One had this beautiful singing voice and she wasn’t allowed to pursue that. My other grandmother, whose wedding ring I’m wearing throughout this awards season, dreamed of being an actress.”

It was the latter grandparent who inspired Close’s first screen performance, back in 1982, in The World According to Garp; she played Robin Williams’s pioneering feminist mother, though she was in fact only four years older than him.

She came to film relatively late, although not for want of trying. She was 35, with an acclaimed stage career to her name, when she was cast in Garp. So while audiences have seen her grow on screen, they never got to see her grow up: her talent arrived fully formed. “Who is this actress who has virtually sneaked up on us?” asked a profile in New York magazine in 1982. By that time, Close already had a Tony nomination, for the musical Barnum, and an Obie award for playing a Victorian woman who lives as a man in The Singular Life of Albert Nobbs, a project she clung to for another 30 years, eventually starring in the 2011 film version. (She is demonstrably tenacious: The Wife took 14 years to reach the screen, and she was attached for the last five of those.)

With Jonathan Pryce in The Wife, which is hotly tipped to win her an Oscar in February. Photograph: Graeme Hunter/Allstar/Sony Picture Classics

Close is unusual for another reason: she got three Oscar nominations in her first three years working in film. After Garp, she was in contention for the baby-boomer comedy The Big Chill and again for the risible baseball drama The Natural. This means that she and the Academy Awards have been inextricably linked since the beginning of her screen career. Add a further three nominations – for playing a spurned lover who turns violent in Fatal Attraction, a scheming noblewoman in Dangerous Liaisons and poor, whimpering Albert Nobbs – and she is closing in on Richard Burton (seven) and Peter O’Toole (eight) for the most acting nods without a win. It is starting to look like a severe case of nominative determinism: Close but no cigar …

The Oscar nominations aren’t announced until tomorrow, although there would be a recount to rival Florida 2000 if Close’s name is not in the best actress category. And although she will face stiff competition, chiefly from Olivia Colman, a co-favourite for The Favourite, there is in The Wife a convergence of encouraging factors. It is a timely subject and a rich, expertly layered performance. Also, it’s about time.

Would it be unseemly to ask what she thinks of her own chances? “Oh, I daren’t even go there,” she laughs. “I’ve survived all this time just being at the party, and I’ve loved it. Most people sweat over whether they’ll actually win, but I’ve never felt that. I think I’ll be incredibly nervous when they open the envelope, but only because so many people will be disappointed if I don’t win. A lot of them already think I’ve got an Oscar. If I do lose, I want to look at the camera and reassure everyone: ‘I’m OK.’”

Whatever happens on the night, it is unlikely to be as dramatic as her experience in 1988, the year of her Fatal Attraction nomination, when she was so heavily pregnant that she attended the ceremony with her obstetrician and his wife in tow. “I had broken my ankle, too, so I had an ankle brace and a cane,” she says. “We were late, there was terrible traffic and we had to get out of the limo and run through the parking lot, and I had lost an earring, so someone had to go back and find it.” Her infectiously jubilant laugh rings out. “When Michael Douglas and I came out to present an award, everyone started laughing at the fact that I was hugely pregnant, because in Fatal Attraction, of course, I keep telling him: ‘I’m going to have your baby!’”

I long for the day when people say: ‘This is a fantastic movie,’ rather than: ‘This is a fantastic women’s movie

The child she was carrying was her daughter, Annie Starke, who is outstanding as the younger Joan in The Wife. The manner in which Close’s pregnancy was reported back in 1987 was indicative of institutionalised misogyny; the popular press tried to portray her as a home-wrecking floozy who couldn’t distinguish between film and reality. “The star of Fatal Attraction has virtually recreated her screen persona by getting pregnant and wreaking havoc in her lover’s life!” reported one UK newspaper. She had first met Annie’s father, the film production manager John Starke, on the set of Garp. Although he was in another relationship when she fell pregnant, it was Close, rather than him, who was singled out for censure by the media.

Close is hopeful now that the fall of Harvey Weinstein and the rise of the #MeToo movement is putting an end to such attitudes, or at least denying them the oxygen of publicity. “I think the effect of it all will be fascinating to see,” she says. “When women have more of a chance, all these great stories are going to come out. And it won’t just be about them. I long for the day when people say: ‘This is a fantastic movie,’ rather than: ‘This is a fantastic women’s movie.’ We have to keep the issue of the empowerment of women at the forefront because it’s something that won’t become part of our culture unless a lot of people fight for it.”

Close has enjoyed her share of complex, challenging parts. She had a ball as the unapologetically savage lawyer Patty Hewes in the TV drama Damages, winning a Golden Globe and two Emmys in the process. Looking back on her career, though, she sees other instances where male perspectives were prioritised. Reversal of Fortune, in which she played Sunny von Bülow, the heiress whose husband Claus (Jeremy Irons) was charged with her murder before being exonerated, was one such example. “That was a script written very much from a man’s point of view,” she says now. “We really didn’t get under Sunny’s skin in that film.” And she has been vocal about the disappointments surrounding Fatal Attraction, from the lack of punishment meted out to the adulterer played by Douglas to the re-shot horror-style climax that transforms Alex, the woman scorned, into an implacable Terminator-like monster. No wonder cinema audiences were baying for Close’s blood, screaming “Kill her!” at the screen as they watched.

Close as Alex in 1987’s Fatal Attraction. Photograph: Everett Collection/Rex Features

“I had so many secrets as Alex,” she reflects. “The woman I was playing was not the same one who was perceived by the public. But I didn’t have the dialogue or the scenes to illuminate her backstory. If you did Fatal Attraction from Alex’s point of view, she would be a tragic person, not a dangerous, evil one.” What a terrific idea, I tell her. Someone should make that version. “We’ve actually approached Paramount about it,” she says. “They have other plans at the moment, but I agree it would be fascinating.” For all its toxicity, Fatal Attraction marked a turning point in the perception of Close. She fought hard to play Alex after executives and producers openly doubted that she could be sexy. And she hurled herself into that picture’s big sex scene. Taking place on top of the washing-up, with the tap running, it threw in everything, including the kitchen sink. Close knocked back margaritas hourly while that scene was being shot – and it took a while.

How refreshing to find her sexuality undimmed in The Wife. The opening sex scene between her and Pryce was the first thing they shot. “We arrived on set in our jammies,” she chuckles. “We were both thinking the same thing: ‘We’re pros, we’ve been doing this a long time. Let’s just get down to it.’” It feels revolutionary to see two actors in their 70s having drowsy, vocal, pleasurably filthy sex together. “I know,” she whoops. “It’s one of the great myths that you lose your sexuality as you get older. One night last year, I was coming across town from the East Village to the West. It was late on a Friday night and there were a lot of couples on the street. Pippy and I were looking out of the car window and I could feel what all those couples were feeling.” Her voice has dropped to an intimate, tingling whisper. “I could feel their excitement, the sense of intimacy about to happen. It was extremely powerful.”

Right now, she believes she is in her prime. “I feel as free and as creative, as sexual and as eager, as I ever have. And it’s ironic because I’m thinking: ‘How much time do I have left now?’ There are so many things I’m interested in doing. It’s one of those ironies, I suppose, that we sometimes start feeling comfortable in our own skin only late in our lives, but hopefully with enough time to benefit from it. I’m so glad to do what I do because even though I’m not a method actor and I don’t use my life in my acting, my work is still a progression. So what comes after this I’m excited to see. Right now, I’m just enjoying feeling …” She searches for the word, then giggles to herself. “Chuffed. Isn’t that what you all say? I’m feeling very chuffed.”

• The Wife is released on DVD, Blu-ray and digital on 28 January