President reportedly told aides and media figures book shouldnt be published before Novembers election
The presidents views on news of a book deal for Marie Yovanovitch, another key figure in the Ukraine scandal which led to Trumps impeachment, were not immediately clear.
Bolton, a former ambassador to the UN, was Trumps third national security adviser until he was fired in September last year.
He refused to testify in the House impeachment inquiry into Trumps attempts to have Ukraine investigate his political rivals, which resulted in two articles of impeachment, concerning abuse of power and obstruction of Congress.
He offered to testify in the Senate but Republicans voted not to call witnesses during a trial which duly ended in Trumps acquittal, despite leaks from Boltons book manuscript seeming to show he possessed key knowledge about the affair.
The Room Where It Happened was slated for publication in March but it has been held up, the national security council telling Boltons lawyer it would move forward as expeditiously as possible with determining what could be published.
On Friday night, the Washington Post cited two anonymous sources as saying Trump had told his own lawyers the book should not come out before the election.
Trump has attacked Bolton publicly on Twitter but the Post also reported notes of an off-the-record briefing of TV anchors on 4 February.
Were going to try and block the publication of the book, Trump reportedly said. After I leave office, he can do this. But not in the White House.
I give the guy a break, he added. I give him a job. And then he turns on me. Hes just making things up.
Trump also called Bolton a traitor, the Post said.
Bolton has begun to discuss his book in public. At Duke University in Durham, North Carolina, on Monday, he reportedly said he was not asking for martyrdom but knew, I think I knew, what I was getting into.
He also said White House efforts to suppress his effort to write history were censorship but did not discuss what he had written in detail.
Bolton has faced criticism for choosing to write his book rather than testify in the impeachment inquiry.
At the Duke event, he answered a question about an infamous July 2019 phone call between Trump and the Ukrainian president, Volodymyr Zelenskiy, with: You will love chapter 14.
At Vanderbilt University in Nashville, Tennessee, on Wednesday, the former Obama national security adviser Susan Rice reportedly told Bolton she could not imagine withholding my testimony with or without a subpoena.
I would feel like I was shamefully violating the oath that I took to defend the constitution against all enemies foreign and domestic, she said.
Bolton said: I said I would testify if subpoenaed. My position is exactly the same as Joe Biden.
Rice retorted: Except Joe Biden didnt have firsthand knowledge about what transpired with Ukraine.