Trump was widely known to record some phone conversations at his office in Trump Tower during his business career, sometimes remarking to aides after a call as to whether or not he had taped that one.
Comey had been invited to testify before a closed session in the wake of his controversial firing by President Trump earlier this week, but declined to do so.
However, Mr Comey believes "if there is a tape, there is nothing he is anxious about", a source told CNN.
Trump began his day on Friday with a series of inflammatory Twitter posts, including a barely veiled threat against Comey, an assertion that it's "not possible" for his spokespeople to accurately represent him, and a suggestion he may end the White House's practice of briefing reporters on most weekdays.
"The point I made with respect to the tweet is the president has no further comment on that", he said. "I think sometimes we don't have an opportunity to get into see him and get his full thinking".
Spicer said he wasn't "aware" of anyone in the White House who has a recording of the dinner while refusing to answer questions about whether Trump is actually recording his meetings.
Spicer said Trump's Twitter message wasn't meant to intimidate Comey. "I think loyalty to the country, loyalty to the United States is important". And on Friday, a person close to the former director recounted a Comey-Trump dinner in January in which Trump asked for a pledge of loyalty.
Trump's latest tweet alluding to the possibility of recordings further added to the heightened drama of the past two days as the White House tries to do damage control on the messaging surrounding Comey's firing.
Comey instead told the Republican president he could count on his honesty, the Times said. But Trump on Thursday acknowledged for the first time that the Russian Federation investigation - which he dismissed as a "made-up story" - was also on his mind as he ousted the man overseeing the probe.
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Trump says Comey had told him three times he was not under investigation in the Russian Federation probe. "In fact", Mr. Trump's tweet came the morning after he asserted Comey had told him three times that he wasn't under FBI investigation.
It's a claim made of Comey that has many experts skeptical.
According to Comey's account to associates, Trump was not satisfied with the Federal Bureau of Investigation director's answer and told him again later in the dinner that he needed Comey's loyalty, the Times reported.
Acting FBI director Andrew McCabe sidestepped a question during a Senate hearing on Thursday on whether he ever heard Comey tell Trump that the president was not the subject of investigation.
He told MSNBC that Comey was uneasy with attending the dinner.
The White House initially cited a Justice Department memo criticizing Comey's handling of last year's investigation into Hillary Clinton's emails as the impetus for Trump's decision.
"Oh, I was gonna fire regardless of recommendation", Trump told NBC's Lester Holt. Reuters White House correspondent Jeff Mason said. On Thursday, Trump told NBC he knew he ran the risk that by firing Comey he would "confuse people" and "lengthen out the investigation" into ties to Russian Federation.
Comey's bureau is investigating whether Russian Federation interfered in the 2016 USA elections and possibly colluded with members of the Trump campaign.
Democrats and some Republicans have expressed concern at the timing of the probe, noting the FBI's current investigation into alleged interference by the Russian government in the USA presidential election.
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