The White House has said the firing was unrelated to the FBI's Russian Federation investigation. Trump was leaving for his first foreign trip, visiting Saudi Arabia, Israel, Vatican, and a pair of summits in Brussels and Sicily.
According to a minute of a meeting read to the New York Times, the USA president said sacking Mr Comey had relieved "great pressure" on him.
Contacted by the Times, White House press secretary Sean Spice did not deny Trump had made the statements, saying Comey's "grandstanding and politicizing" of the Russian Federation probe had put "unnecessary pressure on our ability to engage and negotiate with Russian Federation".
In a potential bombshell, the Washington Post reports that investigators are focusing on a current White House official close to Trump as a person of interest in their probe into the administration's ties to Russian Federation.
The Senate and House intelligence committees are also probing possible collusion between the Trump campaign and Moscow.
Republican Sen. Richard Burr of North Carolina and Democratic Sen.
The report said Trump's comments came from the White House's official written account of the meeting, which included quotations read to the Times with another official confirming the conversation had taken place.
The possibility of a cover-up is the third branch of an investigation that began as a look at Russian meddling in the election and broadened into whether members of the Trump campaign had cooperated in that efforts, according to the briefing, members of Congress said.
House minority leader Nancy Pelosi said Trump has shown his disrespect for the presidency if the Times report is accurate.
Pelosi told The Associated Press in an interview Friday that "every day the president gives us more reason to believe that he does not respect the office that he holds".
"There will not be an announcement of a nominee for Federal Bureau of Investigation director today", the White House said ahead of Trump's departure for Riyadh, his first stop on the five-nation nine days foreign trip.
"Mr.Comey served his country with honour for many years, and he deserves an opportunity to tell his story". The date of the hearing has not yet been set.
The Senate Intelligence Committee hearing will be scheduled after Memorial Day. "I hope that former Director Comey's testimony will help answer some of the questions that have arisen since Director Comey was so suddenly dismissed by the President", Warner said.
Former FBI Director James Comey has agreed to testify to a top Senate committee, an event that could prove a pivotal moment in the fate of President Trump's besieged administration.
Comey will certainly be asked about encounters that precipitated his firing, including a January dinner in which, Comey has told associates, Trump asked for his loyalty. The White House is disputing a report that President Donald Trump asked Comey to shut down an investigation into ousted national security adviser Michael Flynn.
Mr Comey is known to produce memos documenting especially sensitive or unsettling encounters, such as after the February meeting.