President Trump said Saturday that he could name a new FBI director by next week, as five or more candidates are being interviewed at Justice Department headquarters in Washington, D.C.

"I think the process is going to move quickly,” Trump said aboard Air Force One, on his way to give a college commencement speech. “Almost all of (the candidates) are very well known. They've been vetted over their lifetime, essentially. But very well known, highly respected, really talented people and that's what we want for the FBI."

Trump on Tuesday fired FBI Director James Comey.

The president said Saturday a new director could be named by Friday, the day he departs for his first presidential foreign trip.

"That is possible," Trump said en route to give the commencement speech at Liberty University, in Lynchburg, Va.

The first candidate interviewed Saturday was Alice Fisher -- a white-collar defense attorney. Fisher spoke for about 90 minutes with Attorney General Jeff Sessions and his deputy, Rod Rosenstein.

Three other were expected to be interview on Saturday afternoon.

They are acting FBI director Andrew McCabe, Michael J. Garcia, an associate judge on New York's highest court, and GOP Sen. John Cornyn of Texas, the No. 2 Senate leader and a former state attorney general.

However, sources have told Fox News that at least two additional candidates are being interviewed Saturday.

They are Adam Lee, the special agent in charge at the FBI's Richmond office, and Henry Hudson, a district judge of the U.S. Court for the Eastern District of Virginia.

No candidates will be interviewed Sunday, the sources also said.

Trump is considering nearly a dozen candidates to succeed Comey.

Whomever is appointed by Trump would have to be confirmed by the GOP-led Senate.

Fisher was assistant attorney general for the department's criminal division under President George W. Bush.

Fox News' Jake Gibson and the Associated Press contributed to this report.