Trump briefly addressed journalists before flying to Lynchburg, Va., where he delivered a commencement speech at Liberty University.
President Donald Trump will read reports and recommendations from the interviews and then meet with a few leading candidates himself, the official said. He did not interview Saturday, but his name is on the list of people Trump is considering. Replacements for Mr Comey reportedly include current acting Federal Bureau of Investigation director Andrew McCabe, former Republican congressman Mike Rogers, former George W Bush homeland secretary adviser Fran Townsend, former Assistant Attorney General Alice Fisher, special agent Adam Lee, Republican Senator John Cornyn and judges Michael Garcia and Henry Hudson, according to CNN.
In a statement, association president Thomas F. O'Connor said Rogers's background "sets him apart".
The FBI has never had a female director.
At least eight candidates for the bureau's top spot headed to the Department of Justice on Saturday to interview for the position, which was vacated when James Comey was sacked this week. She left after about an hour and a half inside the building and declined to comment to reporters.
Fisher formerly served as assistant attorney general for the Justice Department's Criminal Division.
The Trump administration said Comey was sacked because of how he handled the probe into Hillary Clinton's use of a private email server, though some lawmakers and analysts have suggested the decision may have been related to Comey's separate investigation into Russian interference in the 2016 election. He had been under consideration to take over the bureau on an interim basis, but an official said he is now interviewing for the permanent job. An official said McCabe was aboard one of them. He was the third interviewee of the day.
Trump appeared to suggest on Twitter Friday that there could be recordings.
If loyalty is a key factor in the hiring decision, McCabe might be at a disadvantage.
"Removal of Director Comey only confirms need for select [committee] to investigate", Mr McCain tweeted.
Trump said that one possible alternative to briefings would be, "We do it through a piece of paper with a perfectly accurate, attractive answer".
The candidates interviewing Saturday are among a almost a dozen being considered, the AP reported. "So we can make a fast decision".
"They've been vetted over their lifetime, essentially, but very well known, highly respected, really talented people", the president said.