The White House also steered reporters toward acting FBI Director Andrew McCabe's congressional testimony from last week, in which he seemed to defend both the bureau and the Trump administration in the same breath.
A person who had seen the memo told The Associated Press what Comey had written.
"I hope you can see your way clear to letting this go, to letting Flynn go", Trump told Comey, according to the article. "He is a good guy".
"'I hope you can let this go, '" Trump told Comey of the Flynn investigation, the same source said.
The White House is disputing a report that President Donald Trump asked former FBI Director James Comey to shut down an investigation into ousted national security adviser Michael Flynn.
It continued, "the President has the utmost respect for our law enforcement agencies, and all investigations".
Mr Comey was sacked as FBI Director last week.
Comey was abruptly fired May 9 and learned of the dismissal as he was giving a talk in Los Angeles.
Comey reportedly wrote the memo immediately after he met with Trump, as part of an effort to document situations in which the president sought to interfere in the FBI's operations.
Flynn was sacked on February 13 after it was revealed he had misled Vice President Pence about his conversations with Russian Ambassador to the U.S. Sergey Kislyak about U.S. sanctions recently imposed on Russia; Flynn had been speaking with Kislyak during the transition period between Election Day and Trump's inauguration.
May 12, 2017: Trump tweets that Comey "better hope that there are no "tapes" of our conversations before he starts leaking to the press!" He refused, however, to say whether Trump had discussed making such revelations beforehand with either McMaster or Secretary of State Rex Tillerson.
'He is a good guy, ' Comey remembered Trump saying, acording to the Times.
February 14, 2017: Comey speaks with Trump in the Oval Office a day after Flynn is ousted.
October 28, 2016: Days before the election, Comey informs Congress by letter that he is reopening the investigation into Clinton's email practices based on new evidence, citing the discovery of emails on a laptop used by a top Clinton aide.
The White House has grown suspicious about the volume and timing of the seemingly never-ending stream of leaks about the president, said one senior administration official who spoke on condition of anonymity to reflect on the feeling inside the West Wing. The newspaper cites a memo Comey wrote following the meeting.
Soon after the firing, a Comey associate told the AP that Comey recounted being asked by Trump at a January dinner if he would pledge his loyalty.
After the meeting, Comey's associates did not believe there was any way to corroborate Trump's statements.
House Oversight Committee Chairman Jason Chaffetz, R-Utah, sent a letter Tuesday evening to McCabe requesting all "memoranda, notes, summaries, and recordings referring or relating" to communications between Comey and Trump. On Jan. 26, Acting Attorney General Sally Yates told the White House counsel about the interview, and said Flynn could be subject to blackmail by the Russians because they knew he had lied about the content of the calls.
The turmoil overshadowed Republican legislative priorities such as healthcare and tax reform and laid bare sharp divisions between the White House and US intelligence agencies, which concluded late past year that Russian Federation had tried to influence the 2016 presidential election in Trump's favor.