The document alleges Trump pressured the FBI Director to shut down the investigation into his former National Security Adviser, General Michael Flynn, who was sacked after it emerged he had lied about his conversations with Russia's ambassador to the United States.
The investigation into Flynn coincides with the FBI's examination of alleged collusion between Russia and members of Trump's presidential campaign team.
The New York Times reports Trump asked Comey to end the Flynn investigation during an Oval Office meeting in February.
The Times has not seen Comey's memo, but says one of the former FBI boss's associates read excerpts of it to a reporter.
"I hope you can see your way clear to letting this go, to letting Flynn go," Trump told Comey, according to the memo.
"He is a good guy. I hope you can let this go."
Comey wrote the memo immediately after his meeting with the President the day after Flynn resigned.
"The memo was part of a paper trail Comey created documenting what he perceived as the President's improper efforts to influence an ongoing investigation," the Times reports, pointing out that an FBI agent's contemporaneous notes can be used as credible evidence of conversations in court.
The White House is disputing the accuracy of the report.
"While the president has repeatedly expressed his view that Gen 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," it said in a statement.
"The President has the utmost respect for our law enforcement agencies, and all investigations. This is not a truthful or accurate portrayal of the conversation between the President and Mr. Comey."
It should also be noted that the acting FBI Director, Andrew McCabe, told Congress last week: "There has been no effort to impede our investigation to date."
THE SACKING
Mr Trump fired Mr Comey a week ago. At first, the White House cited Mr Comey's handling of the investigation into Hillary Clinton's email scandal as the reason for his dismissal, but as that story's credibility was called into question, Mr Trump changed tack.
"I was going to fire Comey," he told NBC's Lester Holt. "He's a showboat, he's a grandstander, the FBI has been in turmoil. You know that, I know that, everybody knows that. You take a look at the FBI a year ago, it was in virtual turmoil, less than a year ago. It hasn't recovered from that."
Mr Trump implied the main reason for the sacking was Mr Comey's refusal to scale down his agency's investigation into Russia's interference in the 2016 election - and potential collusion between members of his presidential campaign and the Russian government.
"When I decided to do it, I said to myself ... this Russia thing with Trump and Russia is a made up story," Mr Trump said.
The President's critics claimed he had fired Mr Comey in an effort to stymie the investigation. Mr Trump argued he just wasn't doing a good job.
THE REACTION
"If you are a Republican in Congress, now is the time to panic," CNN political analyst Chris Cillizza said after today's news broke. That pretty much sums up the situation, as the focus shifts to Congress, and whether Mr Trump's political allies will be willing to investigate Mr Comey's paper trail.
At the moment, they appear to be ducking for cover. Most are refusing to comment.
At least one notable Republican, however, has spoken to the media - Jason Chaffetz, who is Chairman of the House Oversight Committee and has the power to investigate Mr Comey's memo.
"On the surface that seems like an extraordinary use of influence to try to shut down an investigation beting done by the FBI," Chaffetz said.
"(We are) going to get the Comey memo, if it exists. I need to see it sooner rather than later. I have my subpoena pen ready."
The committee Chaffetz heads has since sent a letter to the FBI requesting that it provide the memo - and any other relevant materials from Comey.
Another senior Republican figure, former presidential nominee John McCain, openly compared the current situation to the Watergate scandal.
"I think we've seen this movie before. I think it appears at a point where it's of Watergate size and scale," McCain said to former TV anchor Bob Schieffer at a dinner.
"The shoes continue to drop, and every couple of days there's a new aspect," he said.
"Get it all out. It's not going to be over until every aspect of it is thoroughly examined and the American people make a judgment. The longer you delay, the longer it is going to last."
Meanwhile, the reaction on social media was not friendly towards Trump.
THE FIGHTBACK
As the news broke, the Trump reelection campaign - yes, that's already a thing, because America - sent out an email hitting back at both the media, and leakers within the administration.
"You already knew the media was out to get us. But sadly it's not just the fake news ... There are people within our own unelected bureaucracy that want to sabotage President Trump and our entire America First movement," the email reads.
"They don't want it to be America First. They want it to be Special Interests first to enrich themselves while the citizens of our country remain an afterthought.
"We have no choice but to completely DRAIN THE SWAMP. President Trump has already started cleaning house, but every day will be an uphill battle - and we need to be prepared to go into the trenches to FIGHT BACK."
That's what you call a "siege mentality".
