President Donald Trump will interview the former independent senator -- who ran on a ticket with Al Gore in 2000 before endorsing Republican John McCain in 2008 -- at the White House later in the day.
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 now sacked FBI chief James Comey to drop a probe into one of his top advisors.
"He will meet with four more: Andrew McCabe, Frank Keating, Richard McFeely and Joe Lieberman. Those will all happen upon return to the White House this afternoon."
Gore and Lieberman narrowly lost the disputed 2000 election to Republican George W. Bush, and the Connecticut senator mounted his own unsuccessful bid for the Democratic nomination in 2004.
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Lieberman served 24 years as a Connecticut senator before retiring in 2013. He was the northeastern state's attorney general from 1983-88, and also served 10 years in the Connecticut state senate.
Lieberman endorsed Hillary Clinton in last year's presidential election.
The White House has provided no set timeline for the process of replacing Comey. But Trump said Saturday that he would act quickly to appoint a successor.
The president's nominee must be confirmed in the Senate, where Democrats and some Republicans have fiercely criticized Comey's firing.