NEW YORK (NYTIMES) - Jeanine Pirro, the Fox News personality and longtime friend and champion of President Donald Trump, has discussed with him the possibility of a book project to counter the damning portrayal of his presidency in Michael Wolff's book Fire And Fury, according to three people with knowledge of their conversations.

The project has been described among West Wing advisers as No Fire, No Fury, according to two administration officials. Pirro met with Trump in the White House on Wednesday, hoping to secure his participation.

Over lunch, Trump agreed to be interviewed by Pirro for the book, according to one of the people briefed on their discussion.

For weeks, the president has seethed about the depiction of him in "Fire and Fury" as a volatile and ill-equipped chief executive, even asking the White House counsel and allies whether a libel lawsuit against Wolff is still possible. (His advisers have told him no.)

Pirro, 66, who has been friendly with Trump since his tabloid days in the 1980s, is likely to write an account that is highly favourable to him. She has recently emerged as one of his most vociferous defenders - and a frequent visitor to the West Wing.

It was not clear whether Pirro was planning to use the book she has in the works, tentatively titled Liars, Leakers and Liberals, as a vehicle. That book is due out June 12 from Center Street, an imprint of the publishing giant Hachette.

Pirro, in a statement Saturday provided by Fox News, said: "My upcoming book is not a direct response to Fire And Fury. The title on Amazon always has been and continues to be 'Liars, Leakers and Liberals' and I plan to cover all of them."

But inside the White House, Pirro is believed to have pitched her book to Trump as a plum opportunity to present a counterpoint to Wolff. And she has broadly discussed with friends the idea of a book to rebut Fire And Fury. White House aides declined to comment.

Pirro, a former Westchester County district attorney, has not been shy about her newfound proximity to power. On Wednesday, she tweeted a photograph of herself standing by the White House gates.

"Guess where I am?" she wrote.

Pirro, who shares Trump's love of showmanship, has publicly denounced the attorney general, Jeff Sessions, and the special counsel, Robert S. Mueller III.

She delivered a fiery monologue in December on her weekend Fox News programme, Justice With Judge Jeanine, in which she called for FBI and Justice Department officials "to be taken out in cuffs."

But she has pressed her case in private, too, including at an Oval Office meeting with the president in November during which she castigated Sessions and accused the former FBI director James B. Comey of Mafia-style behaviour.

(The president's chief of staff, John F. Kelly, interrupted Pirro and told her that she was not "helping things.")

Pirro's book will have to compete in a crowded Trump publishing marketplace.

Sean Spicer, the former White House press secretary, is releasing an account of his rocky tenure, The Briefing, in July. Under Fire: Reporting From the Front Lines of the Trump White House, by Washington correspondent April D. Ryan, is due in September. Comey's memoir, A Higher Loyalty: Truth, Lies And Leadership, will be released in April.

A spokeswoman for Hachette did not respond to an inquiry Saturday. On its website, the publishing house describes Liars, Leakers And Liberals as "Judge Jeanine's no-holds-barred answer to fake news."

A promotional page says Pirro plans to interview Ivanka Trump, the president's daughter and adviser, and to defend Trump against the news media, which "has twisted his words to fit the narrative they've created." Center Street, Pirro's imprint, is a popular platform for conservatives and allies of Trump. It published Let Trump Be Trump, by the Trump loyalists Corey Lewandowski and David Bossie, last year.

In March, Center Street will release Understanding Trump, an account of the president by Newt Gingrich that includes a foreword by the president's son Eric. The book features an endorsement on its cover from Pirro's colleague at Fox News, Sean Hannity, who calls it "inspiring and informative."