The updates came from Trump as he addressed the media after a White House meeting with Colombian President Juan Manuel Santos.
Rep. Jason Chaffetz announced Thursday he will resign from Congress next month, saying a "mid-life crisis" had compelled him to step away from his chairmanship of the House Oversight Committee just as it is poised to investigate President Donald Trump's firing of the Federal Bureau of Investigation director.
Mr Lieberman was among four candidates Mr Trump interviewed at the White House on Wednesday. Three other potential candidates Trump interviewed on Wednesday are former Oklahoma Gov. Frank Keating, FBI acting director Andrew McCabe and Richard McFeely, a former top FBI official.More news: 'Ozark' Trailer: Jason Bateman Stars in Netflix's New Dramatic Series
In an attempt to quell the furor over Comey's ouster, the Justice Department this week hired former FBI Director Robert Mueller as a special counsel to oversee the investigation.
"I hope (Lieberman) gets chosen, "said Sen". "We don't need anyone who's put on a red shirt or blue shirt - or who's campaigned for president". "I think the question is whether you want someone with a political pedigree or whether you want someone with a law enforcement pedigree". "Unfortunately, Joe Lieberman does not fit that description".
Indeed, John McCain and Joe Lieberman are so close that in 2008 McCain seriously floated the idea of placing Democrat turned Independent Senator Lieberman on the Republican ticket as his running mate.
Considered a moderate with ties to members of both parties in Congress, Lieberman was state attorney general from 1983 till 1989 in CT before being elected to the US Senate from 1989-2013. 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. Senate Republicans lauded Lieberman's possible candidacy, but that support did not extend across the aisle.More news: Sony selects director for 'Spider-Man' spinoff 'Silver Sable and Black Cat'
But Lieberman lost his senate seat to a primary challenger in 2006, and he ran as an independent to retain his seat. He did not seek re-election in 2012.
The White House has denied the allegations. On Thursday the New York Times reported that Comey believed that Trump and his aides had made other inappropriate contacts that he felt compelled to resist.
Several other candidates have withdrawn from consideration, including Rep. Trey Gowdy of SC and Sen.More news: Surprised Alonso gears up for rookie Indy race