Comey told the Senate intelligence committee: "There might be corroboration for our conversation, there might be a tape".
In public testimony before Congress last week, Comey expressed his hope that the tapes did exist.
Trump took to his Twitter account Thursday morning to denounce the report.
In a Rose Garden press conference on Friday, Trump accused Comey of committing perjury for his description of the conversations, and dodged questions on the existence of recordings - though he promised updates to come.
"I think the president made it very clear on Friday that he would get back as soon as possible on this", he told reporters. In both cases, the reporters say, Trump curiously failed to produce the tape.
"I appointed him; I stand by that decision, " he said.
She added: "With all the noise, with all the intensity of the media coverage and obviously what makes headlines, ultimately we're really focused on why the American people elected Donald Trump as their president".
So Trump's tape threat could be a bluff created to get potential witnesses like Comey to question their own recollection of events, fearing that an indisputable tape would come forward and prove them wrong.
Among those in attendance was Rebekah Mercer, the daughter of hedge fund manager and billionaire Robert Mercer whose pro-Trump super-PAC reportedly ran attack ads on Comey.