Those official memos, declassified and yielded to Congress, have now been released.
According to the notes, the president told Mr Comey that he "hadn't stayed overnight" at the Ritz-Carlton but that his concern was "if his wife had any doubt about it".
Immediately after Comey's dismissal, Trump called Comey a "showboat" and a "grand-stander."
"This president is unethical, and untethered to truth and institutional values", Comey said in the book due out Tuesday, a copy of which was obtained by Reuters. I regret that the Post-Dispatch apparently does not share that view.
Comey, whom President Donald Trump fired in May 2017, led the FBI's investigation into Clinton's use of a private email server to conduct official business as secretary of state.
The Trump administration has loudly complained about leaks, and Trump himself has repeatedly accused Comey of being a leaker. I suspect there are millions of Americans who would agree.
In a January 28, 2017, memo released Thursday, Comey said Trump castigated Flynn for not promptly scheduling a return phone call of congratulations from a foreign head of state.
"He [Mr Trump] replied by saying it may involve putting reporters in jail".
Trump has disputed Comey's accounts of their conversations.
President Trump ripped "Shadey" James Comey and defended disgraced Michael Flynn on Friday. "Is that really the way life in America is supposed to work?"
He added, "I think he will be prosecuted".
At a meeting in Trump Tower in NY just days before Mr Trump's inauguration in January 2017, Mr Comey spoke alone with the then president-elect about details of an alleged encounter involving prostitutes in Russian Federation.
They also refer to Trump's denials of a salacious incident with prostitutes in Moscow in 2013, which was included in a dossier by former British spy Christopher Steele. "I have never met him and I don't know what he will do on the worldwide arena".
Comey recounts an Oval Office conversation from February 2017 in which Trump raises the prospect of jailing journalists who benefit from leaked information. The memos have been turned over to Mueller.
Comey said he "paused for a few seconds and then said that I would answer here, but that this illustrated the kind of question that had been asked and answered through established channels".
JOHNSON: (Laughter) Jim Comey's been on the air nonstop with his new book. "He seems to me too smart of a man to make a mistake like this". Flynn pleaded guilty to lying to the FBI and is now cooperating with Mueller's investigation.
Comey's response is redacted in the unclassified memos. The FBI has determined that some of that information was classified, said a person familiar with the matter.
The "witch hunt" won't be over until the mother of all investigations surrounding the Trump family and its 2016 campaign contacts with Russian Federation is over. They predicted that the memos would help investigators piece together a case against Mr. Trump and his associates. He called him "morally unfit".
In an offshoot of the Mueller probe, Trump's longtime personal lawyer's office and home were raided by the Federal Bureau on Investigation on Monday.