The New York Times was the first to report the discussion and subsequent memo Tuesday.
In the memo, which Comey shared with top FBI associates, the former director wrote that Trump said, "I hope you can let this go," in relation to the inquiry into Flynn's actions.
“I hope you can see your way clear to letting this go, to letting Flynn go,” said Trump to Comey, according to the source who read the memo. “He is a good guy. I hope you can let this go.”
ABC News has not seen the memo and Comey has not commented on the matter.
Multiple sources who have worked closely with the former director, including within the Justice Department, say Comey is known for his fastidious notetaking.
"He documents everything," one source said.
The alleged request from Trump came the day after Flynn was forced to resign after misleading the administration about his contact with Russian officials. The FBI, which is investigating Russian interference into last year's presidential election, declined to comment on the story.
The White House denied that the request took place in a statement that notes “while the president has repeatedly expressed his view that General Flynn is a decent man who served and protected our country, the president has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving General Flynn.
“The president has the utmost respect for our law enforcement agencies, and all investigations," continues the statement. "This is not a truthful or accurate portrayal of the conversation between the president and Mr. Comey.”
A White House official further emphasized that acting FBI Director Andrew McCabe gave testimony to the Senate Intelligence Committee last week in which he said, "There has been no effort to impede our investigation to date."
On Tuesday evening, Rep. Jason Chaffetz, R-Utah, the chair of the House Oversight Committee, sent a letter to McCabe requesting that the FBI provide "all memoranda, notes, summaries, and recordings referring or relating to any communications between Comey and the President" by May 24. Earlier in the night, Chaffetz tweeted that he has his "subpoena pen ready."
All 33 Democrats on the House Oversight and Judiciary Committees penned additional letters to the chairmen of both panels demanding an investigation into the actions of Trump, Attorney General Jeff Sessions and top White House aides -- and whether they "engaged in an ongoing conspiracy to obstruct the criminal, counter-intelligence, and oversight investigations" into the Trump campaign at the Justice Department and on Capitol Hill.
Trump fired Comey, not yet four years into his 10-year term, last week and admitted later he was thinking about the Russia investigation when he made the decision. The White House originally pegged the president's decision on the recommendation of Sessions and Deputy Attorney General Rod Rosenstein, but Trump himself pushed back, saying it was his decision alone.
On Friday, after details of a January dinner between Comey and Trump emerged in which the president is said to have asked Comey for his loyalty, Trump tweeted a warning to Comey.
"James Comey better hope that there are no 'tapes' of our conversations before he starts leaking to the press!" he wrote.
The administration declined to comment on the existence, or lack thereof, of recording devices in the White House. Associates of Comey told ABC News Sunday that he believes that public testimony before Congress is the most appropriate setting to share details of his termination.
Tuesday is the second day in a row that the administration is pushing back on a damaging headline. On Monday, The Washington Post reported that Trump shared classified intelligence with Russian officials visiting Washington, D.C., last week.
ABC News' Jack Date and Benjamin Siegel contributed to this report.