Bolton alleges Trump asked him to call Zelenskiy to "ensure Mr. Zelenskiy would meet with Mr. Giuliani, who was planning a trip to Ukraine to discuss the investigations that the president sought," according to the Times' description of the book. Bolton writes he never placed the call, the Times account said.
ABC News has not independently reviewed Bolton's manuscript.
In a statement to the New York Times, given after the article was published, Trump categorically denied Bolton's account.
“I never instructed John Bolton to set up a meeting for Rudy Giuliani, one of the greatest corruption fighters in America and by far the greatest mayor in the history of N.Y.C., to meet with President Zelensky," Trump said. "That meeting never happened.”
On May 10, Rudy Giuliani did send a letter to President Zelenskiy -- saying he was acting with the "knowledge and consent" of President Trump-- requesting a meeting with the newly elected president.
The date of that letter, turned over to House investigators by Lev Parnas, an indicted associate of Giuliani, would appear to match the general timeline Bolton describes.
Giuliani also denied Bolton's account on Friday.
Bolton is “Lying to sell his book and get revenge on those he thinks fired them," Giuliani told ABC News. "The latest is false.”
The report comes just as the Senate is set to vote on whether to call witnesses, including Bolton, in Trump’s impeachment trial before closing arguments and a final vote on acquittal. It is not yet clear what effect the report might have on senators.
Democrats need four Republicans to vote with them in order to reach a majority necessary to win on calling witnesses, but it appears they do not have the votes to do so.
Republican Sen. Lisa Murkowski of Alaska announced just after the report surfaced that she would be voting against hearing witnesses, leaving Democrats likely short of the 51 votes they need.
Late Thursday night, key Republican Sen. Lamar Alexander of Tennessee announced he would not vote in favor of calling witnesses in the trial.
Republican Sens. Susan Collins of Maine and Mitt Romney of Utah both announced they would vote in favor of calling witnesses.