"I still need to speak with him so this comes with a big asterisk on it as to whether it happens as we planned," Chaffetz said Wednesday.
Trump fired Comey on May 9 and later insisted that he was going to jettison the FBI director no matter what the attorney general or deputy FBI director recommended.
The FBI has been investigating Russia's meddling in the U.S. election and whether there was any collusion with Trump associates. Flynn, a retired Army general, was dismissed from his job less than a month into the new administration after misleading Vice President Mike Pence about his conversations with the Russian ambassador regarding U.S. sanctions against Russia.
The FBI is probing whether Flynn broke any laws.
Comey wrote in a memo, first reported by The New York Times and confirmed by several other news outlets, that Trump asked him during an Oval Office meeting in February to lay off Flynn.
The Senate Intelligence Committee, which is investigating Trump associates' ties to Russia and its interference in the U.S. election, has also asked Comey to testify. The Senate Judiciary Committee is considering doing the same.
White House press secretary Sean Spicer said Wednesday that the president "wants to get to the bottom of this" but did not respond to questions about whether Trump wanted Comey to testify.
"He wants the truth and these investigations to get to the bottom of the situation," Spicer said aboard Air Force One.
Spicer continued to push back on Comey's claim of what Trump said in their meeting.
"The president has been very clear," Spicer said, "that this is not an accurate representation of that meeting."