Mr. Trump told reporters on Air Force One that he may select Comey's successor before leaving for his first foreign trip next week.
"I think the process is going to go quickly", Trump added before flying to Lynchburg, Va., to deliver Liberty University's commencement address. They've been vetted over their lifetime, essentially.
FBI Director James Comey, left, was abruptly "terminated" by US President Donald Trump earlier in the week.More news: Police chief shot in Orange County; suspect reported to be dead
"Listen, I don't have the foggiest whether there are tapes are not, but the fact that the president made allusions to that and then the White House would not confirm or deny, it is not anything we have seen in recent days", Warner told ABC's "This Week" on Sunday.
Among those expected to be coming in Saturday are acting Federal Bureau of Investigation director Andrew McCabe and Alice Fisher, a top Justice Department official in the George W. Bush administration.
The decision is subject to confirmation by the U.S. Senate, where Republicans have a majority.More news: Intel Will Introduce The i9 Series Later This Year
The White House initially said Trump was compelled to fire Comey after a critical memo from the deputy attorney general on the director's handling of last year's investigation into Clinton's use of a private e-mail server.
Adam Lee, special agent in charge of the FBI's Richmond, Virginia, office, was also interviewing Saturday afternoon. Trump's dismissal letter to Comey says the move was necessary "to restore the public's trust and confidence in its vital law enforcement mission".
Trump fired Comey on Tuesday, and the president said in an NBC News exclusive interview on Thursday that he had been planning to do so regardless of what the Department of Justice recommended.
A separate report from the Associated Press found the Senate intelligence committee had subpoenaed former Trump national security adviser Michael Flynn for documents related to the panel's investigation into Russia's election meddling. He thanked the crowd for their support and repeatedly invoked his own unlikely election victory.More news: North Korea: New long-range missile can carry heavy nude
"You can't be cute about tapes", Graham said. "Nothing is easier or more pathetic than being a critic, because they're people that can't get the job done".