Trump says 'fast decision' on new FBI head is possible as candidate interviews underway

— -- President Trump said his administration may be able to "make a fast decision" on a new FBI director as candidates began arriving at the Department of Justice Saturday morning for interviews.

"We can make a fast decision," Trump told reporters Saturday of the administration's search for a replacement for fired FBI Director James Comey.

Asked if there will be a decision before the start of the president's foreign trip on May 19, he said, "Even that is possible."

Trump said nearly all of the candidates under consideration "are very well known, so you know they've been vetted over their lifetime essentially."

The president added that candidates under consideration for the post are "highly respected, really talented people."

Trump spoke to reporters aboard Air Force One as he was on his way to Virginia to give the commencement address at Liberty University as meanwhile interviews for the FBI director position were underway at the Justice Department in Washington, D.C.

Adam Lee, special agent in charge of the FBI's office in Richmond, Virginia, whom sources told ABC News would be interviewing for the FBI job, arrived at the Justice Department around 1 p.m. Saturday.

Earlier, Alice Fisher, a former assistant attorney general in charge of the Justice Department's criminal division, was the first candidate to go for an interview with Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein.

Fisher, who emerged from the meeting over an hour later, would be the first female FBI director if appointed.

In addition to Fisher and Lee, ABC News has learned that Sen. John Cornyn, R-Texas, Judge Michael Garcia of the New York Court of Appeals and Acting FBI Director Andrew McCabe are expected to be interviewed Saturday with others to follow in the coming days.

On Saturday, the The FBI Agents Association (FBIAA) urged Trump to nominate former House Intelligence Committee Chairman and FBI Special Agent Mike Rogers. A CNN national security commentator, Rogers represented Michigan's 8th congressional district in the House from 2001 to 2015.

"Chairman Rogers exemplifies the principles that should be possessed by the next FBI Director,” said FBIAA President Thomas F. O’Connor. “It is essential that the next FBI Director understand the details of how agents do their important work. Mike Rogers’ background as a special agent, veteran of the armed forces and former member of Congress sets him apart as someone capable of confronting the wide array of challenges facing our help ensure that the bureau remains the world’s premiere law enforcement agency.

"Rogers’ unique and diverse experience will allow him to effectively lead the men and women of the bureau as we work to protect our country from criminal and terrorist threats," O’Connor added. “During his time in Congress he showed a commitment to confronting threats to our country in a nonpartisan and collaborative manner.”

The FBIAA represents over 13,000 active and retired agents.

Here is the full list of candidates being considered for the post, listed in no particular order. The list was first reported by Fox News. Sources caution that the list is fluid and could change.

- Ray Kelly, former New York City police commissioner (Kelly is also an ABC News contributor)

- Mike Rogers, former House Intelligence Committee chairman. Rogers worked as an FBI agent but retired in 2015.

- Alice Fisher, former assistant attorney general

- Adam Lee, special agent in charge of the FBI's office in Richmond, Virginia

- Rep. Trey Gowdy, R-South Carolina

- John Cornyn, Senate majority whip, R-Texas

- Paul Abbate, executive assistant director for the Criminal, Cyber, Response and Services branch of the FBI

- Michael Garcia, former New York prosecutor, now associate judge on New York Court of Appeals

- John Suthers, mayor of Colorado Springs

- Michael Luttig, former federal appellate court judge and now executive vice president of Boeing

- Larry Thompson, former deputy attorney general under President George W. Bush

- Andrew McCabe, acting FBI director

ABC News' Jack Date, Katherine Faulders, Jonathan Karl, Pierre Thomas and Mike Levine contributed to this story.