Joe Lieberman his top pick.
Andrew McCabe, now the bureau's acting director; and Richard McFeely, a former top FBI official, also went to the White House for interviews on Wednesday.
Trump clearly knew what he wanted to say as he took a few questions at a news briefing with visiting Colombian President Juan Manuel Santos.
Trump said that Comey "was very unpopular with most people" and said that he was expecting more widespread praise for the firing. The president has suggested he hopes to name Comey's successor before he departs Friday for his first overseas trip as president.
Now, Lieberman works in the same law firm as Trump's longtime lawyer, Marc Kasowitz. They are acting FBI Director James McCabe, Senate Majority Whip John Cornyn, a former assistant attorney general Alice Fisher and Judge Michael J Garcia of the New York Court of Appeals. He also disputed the administration's characterization of an investigation into potential coordination between Russian Federation and the Trump White House. "I'm somebody who spent a lot of time in law enforcement; this is a moment where we need a law enforcement professional that's never campaigned for a presidential candidate, never campaigned for office, never worn a party label to head the Federal Bureau of Investigation". The White House says President Donald Trump will be interviewing four p.
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"I think Joe Lieberman is a pillar of credibility", Graham said. "Everybody likes and respects Joe Lieberman".
But several Democratic senators said during a caucus lunch Thursday that they would not support Mr Lieberman, according to a person familiar with the meeting who declined to be identified because the lunch was private.
Trump has been scrambling to find a new FBI chief since he abruptly fired former FBI Director James B. Comey on May 9. Mr Flynn has figured prominently in the FBI investigation into Russian interference into the election.
Among their concerns was Mr Lieberman's past praise of Mr Michael Flynn, Mr Trump's first national security adviser, who was sacked in February after misleading officials about his conversations with Russian officials.
Since retiring from the Senate in 2013, Lieberman has worked for the NY law firm, Kasowitz Benson Torres and Friedman that has included Trump as a client. Mr Lieberman testified in support of Mr Sessions at his January confirmation hearing.
Lieberman was Democrat Al Gore's vice presidential nominee in 2000 and unsuccessfully ran for the Democratic presidential nomination in 2004. Lieberman abandoned his party after he lost his 2006 primary to Ned Lamont, and he lost that election mainly because of his zealous support for the Iraq war and his perceived closeness to Bush in connection with that. John McCain's presidential bid in 2008 over Barack Obama, speaking at the Republican National Convention that year.