Trump and Lieberman discussed the position at the White House on Wednesday.
The meetings come more than a week after Trump fired FBI Director James Comey. John McCain in his race against Barack Obama in 2008.
Former Democratic vice presidential candidate, former Connecticut Sen. "It's special", Trump said later at a joint news conference with Santos.
Lieberman, a Democrat turned independent from CT and a former attorney general for the state, just entered the candidate mix Wednesday.
During last year's presidential campaign, he criticized Trump for his lack of leadership and once referred to him as "hysterical".More news: Smalling sees positive in Mourinho criticism
He spends some time at a Manhattan law firm and helps lead No Labels, an organization devoted to promoting bipartisanship - a Lieberman calling card.
McCabe, until he became acting director when Comey was ousted, had been the agency's deputy director.
Lieberman now works at the law firm that often represents Trump, Kasowitz.
Keating, the governor of Oklahoma during the 1994 bombing of the federal building in Oklahoma City, left the White House with a smile on Wednesday.
A White House official told Fox News last week that they are working "quickly and expeditiously" and doing their "due diligence".
Comey was investigating the Trump campaign for possible collusion with Russian operatives to influence the 2016 election, and his termination fueled speculation that Trump was attempting to impeded the bureau's probe.