But Trump said Saturday that he would act quickly to appoint a successor.
The former senator from CT says he got an unexpected call to interview for the position on Tuesday. Joseph Lieberman as his running mate, making him the first Jewish candidate on a major party ticket. Trump responded, "He is".
White House Press Secretary Sean Spicer confirmed that the Trump administration has been interviewing candidates to replace former FBI Director James Comey after his firing early last week.
But he also said there had been "no effort to impede our investigation to date" - which would seem to be good news for a White House that now faces suggestions that the president might have attempted to obstruct justice.
Mr. Trump is also considering former Republican Oklahoma governor Frank Keating, acting FBI Director Andrew McCabe, and former FBI official Richard McFeely.
W.House denies Trump caused 'lapse in national security'
The information had been supplied by a USA ally in the fight against the Islamic State militant group, the officials said. Such sharing "could be a risk for our sources", the official said, the Associated Press reports .
Former Sen. Joe Lieberman is President Donald Trump's top pick to be nominated as Federal Bureau of Investigation director, Trump said Thursday.
Cornyn, who the officials say was intrigued by the idea and initially interested, ultimately withdrew from consideration after a number of his colleagues said they believed Trump should shy away from picking a GOP politician.
Trump criticized Comey for a recent performance testifying to Congress and said Comey's replacement is "going to be outstanding".
Lieberman spent 24 years in the Senate, entering as a Democrat in 1989 and leaving as an Independent in 2013. He supported Sen. John McCain for president in 2008, but endorsed Hillary Clinton in 2016, a move that could count against him with Trump, who screens candidates for his administration for loyalty. He has served as co-chairman of No Labels, a centrist group that promotes bipartisanship.
He was the lead case agent on the Oklahoma City federal building bombing in 1995, when Keating was governor, and he was the FBI's on-scene commander after the September 11, 2001, attack on the Pentagon. The firing also came as Comey was leading investigations into allegations that the Trump campaign and transition team had inappropriate contacts with Russian Federation.
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