The president reportedly made the comments during a private meeting with the FBI director in which he also suggested the bureau should drop its investigation into Michael Flynn.
Trump attempted to persuade the former FBI director to drop the probe into Michael Flynn's links to Russia, The New York Times reported, citing a memo Comey wrote.
Erwin Chemerinsky, dean of the University of California, Irvine Law School, has joined other prominent attorneys in filing suit against Trump for his alleged breach of the emoluments clause.
The president tweeted: "James Comey better hope that there are no 'tapes' of our conversations before he starts leaking to the press!" Claims about Trump's past actions indicate there may be.
Senator Casey: My gravest concern is the profound chilling effect that the firing of Director Comey may have on the FBI's investigation into the Trump campaign's ties to Russia
The president made reference to possible recordings of his conversations with the former FBI director.
Trump's efforts to politicize the FBI and other American institutions could set a dangerous precedent for future leaders.
The president claimed he was planning to fire FBI director Comey regardless of the DOJ's advice. But the majority of Americans do not approve of Trump's decision.
Senate Democratic Leader Chuck Schumer said his caucus has not yet made a decision on whether to withhold their votes, but added that the issue is being looked at as a way to ensure there is a thorough investigation of alleged Russian meddling in the 2016 U.S. election.
This weekend's Sunday shows found it hard to locate a member of Trump's administration willing to explain his decision to fire FBI director James Comey, as the president appeared to mull becoming his own press secretary.
"I think the process is going to go quickly," Trump said, adding that the candidates under consideration were mostly well known. "They've been vetted over their lifetime essentially."
Trump contradicted White House statements on Comey's termination but said he wanted the Russia probe to be "so strong and so good."
Sources have named Ayotte as a possible successor to the role, but two high-profile Trump allies are not in contention.
Meanwhile, the FBI raids the offices of a GOP fundraiser with links to Trump.
President says the former FBI director was a 'grandstander' who was going to go no matter what Jeff Sessions and Rod Rosenstein recommended.
Former FBI Director James Comey had been scheduled to speak at the Senate Intelligence Committee hearing before his firing.