Sources told ABC News that Trump posed the question to Comey more than once during a dinner in January and Comey would not promise such a thing to the new president, only that he would be honest.
"I didn't ask that question," Trump said in an interview with Fox News' Jeanine Pirro that aired Saturday night.
Trump, however, said it "wouldn’t be a bad question to ask."
When asked about his Friday morning tweet that Comey "better hope that there are no 'tapes'" of their conversations, Trump said, "Well, that I can't talk about."
In a sudden move late Tuesday night, Trump fired Comey, who had six more years left in his term. Trump said he had been thinking about dismissing Comey ever since he took office, but there was never going to be an appropriate time to do it.
"Let's say I did it on January 20, the opening, right, and that would have been the big story as opposed to the inauguration," Trump said. "I was thinking about it then. I was thinking about it during this period of time. There's really no right time to do it."
Trump added, "But I mean, I'm OK with it."
In the initial moments after Comey’s firing, Trump's press secretary, deputy press secretary and Vice President Mike Pence all said Trump's decision was based on the recommendation of Deputy Attorney General Rod Rosenstein. But on Friday, Trump contradicted his press office and Pence, telling NBC that he was going to fire Comey "regardless" of Rosenstein's recommendation.
Asked about the differing statements he and his White House offered, Trump said, "Well, that's an interesting situation," and admitted he toyed with the idea to stop White House press briefings.
"I actually said today, let's not ever do any more press briefings," Trump told Fox News.
But then Trump went on to argue that his administration's press briefings get high ratings and that networks would "start to cry" if he canceled them.
"These press conferences are like the biggest thing on daytime television," Trump said.
Pressed by Pirro on whether he was seriously considering doing away with the press briefings, Trump suggested he would conduct them in a "different way" -- either giving the press "a piece of paper with a perfectly accurate, beautiful answer," or holding them himself.
"We just don't have them, unless I have them every two weeks and I do myself. We don't have them. I think it's a good idea," Trump said.
Trump argued the hostility he feels from the press and because he’s such an active president that his spokespeople cannot keep up with him are reasons to consider getting rid of press briefings.
In the wake of recent reports that Trump is considering replacing his press secretary Sean Spicer, Trump defended Spicer as a “wonderful human" and a "nice man."