Asked whether the 75-year-old was a frontrunner, Trump responded "yes" - confirming Lieberman's surprise candidacy.
Lieberman, a former independent senator from Connecticut, ran on a ticket with Democrat Al Gore in 2000, but they were defeated by George W. Bush and Dick Cheney.
In 2008, Lieberman endorsed Republican John McCain.
The choice of a new FBI director will be closely scrutinised with the administration thrown into turmoil by a succession of stunning allegations against Trump, most damagingly that he may have obstructed justice by asking Comey to drop a probe into one of his top advisors.