The Watergate reporter Bob Woodward is writing a follow-up to Fear, his 2018 bestseller on the Trump White House – and this time, the president has decided to talk.

Donald Trump let the news slip during a controversial interview with the Fox News host Laura Ingraham which was broadcast on Friday.

“I was interviewed by a very, very good writer, reporter,” Trump said. “I can say Bob Woodward. He said he’s doing something and this time I said, ‘Maybe I’ll sit down.’”

Woodward conducted hundreds of interviews for Fear: Trump in the White House, which became a bestselling story of extreme White House dysfunction in the first year of the Trump administration.

Famously, he opened the book with Gary Cohn, then Trump’s chief economic adviser, removing a paper from the Resolute Desk in the Oval Office, lest the president do something extreme.

But he didn’t talk to Trump, despite repeated requests.

Fear: Trump in the White House. Photograph: AP

Fear came out in September 2018, eight months after Michael Wolff’s explosive Fire and Fury set off a Trump book publishing boom that has never truly died down.

Trump greeted Woodward’s book with derision, calling it “a piece of fiction” and a “con of the public” and its author a “liar” with “phoney sources”.

But the president is nothing if not changeable and on Sunday, one of Woodward’s chief competitors, Maggie Haberman of the New York Times, tweeted that Trump has “met with Woodward at least twice for his second book; Woodward, a legend, is now ‘very good’.”

When Fear came out, Sarah Sanders, then White House press secretary, claimed its sources were mostly “former disgruntled employees”.

On Sunday, the Post’s Josh Dawsey duly reported that “Trump has also told skeptical senior aides to cooperate with Woodward this time.”

Nearly 50 years have passed since Woodward and Carl Bernstein took down a president, a story they chronicled in the books All the President’s Men and The Final Days. Woodward, now 76, took the fuss around Fear in his stride.

Speaking to the Guardian, he remembered Ron Ziegler, Richard Nixon’s press secretary, saying he and Bernstein were “character assassins”.

“Trump and these people have said lots of things,” he said. “I haven’t heard character assassin. That’s bracing.”

Woodward also said he thought “too many people have lost their perspective and become emotionally unhinged about Trump”, and said he was dedicated to reporting “what really happened”.

“I look at my job,” he said, “as let’s present the rock-solid evidence of what happens. There’s documents, there’s notes, there’s not just the phrase but there’s where they sat and they met and this is what happened. Let the political system respond.”

Two years on, the political system has responded to Trump: he has been impeached by the Democratic-controlled House and awaits trial in the Republican Senate. Furthermore, by ordering the assassination of the Iranian general Qassem Suleimani, Trump has precipitated the kind of international crisis that haunted the pages of Fear.

When Fear was released, Trump suggested he might write a book of his own. No such tome has appeared although last week the president made news by saying he wanted to buy one of the many books about him: Donald J Trump: An Environmental Hero by Edward Russo.

Now he has spoken to Trump, Woodward will doubtless double-source all the president’s claims.

“Trump had one overriding problem,” Woodward wrote in Fear, “[which John Dowd the president’s personal lawyer] knew but could not bring himself to say: ‘You’re a fucking liar.’”