He briefly served in the agency in the 1970s, and was also in consideration for the director position in 2001, when then-director Louis Freeh resigned.
Speaking to reporters today, Trump said the longtime Connecticut Senator is the "frontrunner" to replace James Comey, who was sacked last week by the President. McCabe was tapped to become acting director after Trump dismissed Comey on May 9. He's worked for a NY law firm that has long represented Donald Trump. He said the bureau hasn't enjoyed "that special reputation" since during the presidential campaign. Trump has promised to name James Comey's replacement soon.
In 1998, Lieberman gave a scathing critique of President Bill Clinton over his affair with White House intern Monica Lewinsky on the floor of the Senate. But with strong support from his close friend, Democratic leader Harry Reid of Nevada, Lieberman kept his chairmanship.
South Carolina Senator Lindsey Graham, a Republican, told reporters on Thursday that he would support the pick. "Everybody likes and respects Joe Lieberman". In a statement Tuesday, the Senator said, "I've informed the administration that I'm committed to helping them find such an individual, and that the best way I can serve is continuing to fight for a conservative agenda in the U.S. Senate".More news: Senate intel chairman: No decision from Flynn on honoring subpoena
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There are early signs that Senate Democrats will seize on Lieberman's political career as a black mark against him. Flynn has figured prominently in the FBI investigation into Russian interference into the election. He made headlines in 2000 as Vice President Al Gore's running mate in a contest that made him the first national Jewish candidate.
After losing the Democratic primary in his 2006 reelection bid, Lieberman left the party and mounted a bid as an Independent, winning the three-way race by 10 percentage points.
Many liberal Democrats are still bitter about Lieberman's stance in publicly supporting Republican John McCain against Democrat Barack Obama in the 2008 presidential race and for strongly supporting the Iraq War under Republican President George W. Bush. He has served as co-chairman of No Labels, a centrist group that promotes bipartisanship.
Keating, a Republican, was a two-term governor of Oklahoma and led the state during the deadly 1995 bombing of the Oklahoma City federal building.
Trump and Sessions also interviewed former Oklahoma Gov. Do you think they need to tone it down?