Four potential candidates to lead the FBI — including former Connecticut Sen. Joe Lieberman — have met with President Donald Trump and Attorney General Jeff Sessions.

Former Oklahoma Gov. Frank Keating; Andrew McCabe, currently the bureau's acting director; and Richard McFeely, a former top FBI official, also went to the White House for interviews on Wednesday.

The meetings came more than a week after Trump fired James Comey from his post as FBI director.

Trump said Monday that the search for a successor to Comey was "moving rapidly." He also has said he could name a candidate by the end of the week, before he departs Friday afternoon on his first overseas trip as president. The Senate must confirm whoever Trump nominates.

Press Secretary Sean Spicer informed reporters about the meetings as Trump flew to Washington after addressing U.S. Coast Guard Academy graduates in Connecticut.

Asked as he left the White House whether he would say 'yes' if Trump offered him the job, Keating said, "I'm a public servant." He added, "Let's just say we had a good conversation."