He offered to furnish a "record" of the Trump-diplomats meeting in the Oval Office if the White House desired it.
Lieberman's front-running status, first reported by Politico, followed the former senator's Wednesday meeting with Trump.
"Like everything else, this was to be expected, President Trump is keeping his promise", Lieberman, the former chairman of the Senate Homeland Security Committee, told Business Insider in an interview.
Trump and Lieberman discussed the position at the White House on Wednesday.
Trump also interviewed former Oklahoma Gov. Somewhere along the way, though, Lieberman seems to have lost the favor of his fellow Senate Democrats, as Politico reported Thursday that many of his former colleagues reject the notion that he could lead the Federal Bureau of Investigation. If his nomination is made official, Lieberman would have to be approved by the Senate Judiciary Committee, then confirmed by the full Senate.
The White House initially claimed Comey's firing was tied to Comey's "mishandling" of the investigation of Hillary Clinton use of a private email server and her handling of classified information during her tenure as secretary of state. With an unpredictable political record, Lieberman may not totally please either side of the aisle.
However another answer on that subject seemed both more specific and perhaps ambiguous.
Democrats, however, may not love their former vice-presidential candidate, who ran alongside Al Gore in 2000. When asked if Lieberman was among the finalists, he said "Yes" emphatically, and anonymous sources have told several news outlets Lieberman is his top choice.
Later, Trump said he had been planning for months to sack Comey. His only law enforcement experience came in the six years before his ascent to the Senate, during which he served as as Connecticut Attorney General. He also publicly disagreed with Trump's so-called Muslim ban. After losing the Senate primary in part because of Connecticut Democrats' betrayal and unwillingness to support a so-called moderate, Lieberman ran as an Independent and won by 10 percentage points. John McCain (R-AZ) and Lindsey Graham (R-SC).
In December 2010, for instance, Lieberman successfully pressured Amazon.com and the data visualization site Tableau to stop publishing charts that included materials believed to have originally been posted by WikiLeaks. He has served as co-chairman of No Labels, a centrist group that promotes bipartisanship. Keating earned a law degree from OU, and has also worked under former presidents Ronald Reagan and George H.W. Bush.
Several candidates have withdrawn from consideration: Rep. Trey Gowdy, R-S.C.; Cornyn; Alice Fisher, the former head of the Justice Department's criminal division; and Michael Garcia, a former USA attorney from Manhattan.