House Speaker Paul Ryan of Wis. takes questions from reporters at the Republican National Committee Headquarters in Washington, Wednesday, May 17, 2017.
Lieberman, the left-leaning Democratic Party's vice presidential nominee in 2000 who later was re-elected to the Senate as an independent, met with Trump on Wednesday at the White House.
Trump also said he "respects" the decision to appoint a special counsel to investigate the Trump campaign's ties to Russian Federation, but he didn't distance himself from his earlier description of the situation as "a witch hunt".
The White House declined to comment to Politico, while Lieberman's office had not yet replied as of the publication of its story. Lieberman was the first Democratic senator to criticize former President Bill Clinton publicly during the Monica Lewinsky scandal.
President Donald Trump said on Thursday he was close to selecting a new Federal Bureau of Investigation director and that former senator and Democratic vice presidential candidate Joe Lieberman was among the top candidates. Not because we don't respect Joe Lieberman.
SCOTT HORSLEY, BYLINE: Trump held that meeting with foreign minister Sergey Lavrov just one day after he had abruptly fired Jim Comey.
Trump said "soon" when asked how close he is to making an announcement.
When asked if Lieberman was his top pick, the president said "yes". They are acting FBI Director James McCabe, Senate Majority Whip John Cornyn, a former assistant attorney general Alice Fisher and Judge Michael J Garcia of the New York Court of Appeals. Charles E. Schumer, New York Democrat, said on the chamber floor. In January, he said he wasn't surprised that Trump delivered on his campaign promise to restrict the travel of people from some terrorism hotspots to the US. A late and somewhat unlikely addition to Trump's short list, Lieberman is nonetheless the sudden frontrunner.More news: Merkel: British EU immigration cap would have price
Lieberman's past law enforcement experience would mainly come from his time as Connecticut Attorney General from 1983 to 1989.
Republicans, by contrast, praised Lieberman. Sen. Lieberman spent most of his career as a Democrat, and there are some who thought that nominating Lieberman might win bipartisan support.
The Justice Department says Mueller, the new special counsel, has been given sweeping power to investigate Russian interference in the 2016 presidential campaign, including potential links between Moscow and Trump associates.
Lieberman has weighed in on some points of Trump's agenda since his election.
Neera Tanden, president of the Center for American Progress, a Democratic think tank, said Lieberman lacks law enforcement experience and is too close to Attorney General Jeff Sessions, a former USA senator. Lieberman testified in support of Sessions at his January confirmation hearing.
Lieberman represented CT in the Senate from 1989 to 2013, initially as a Democrat. He also backed Republican Sen. John McCain (R-AZ) and Lindsey Graham (R-SC). He has spent part of his time as the co-chairman of a group called No Labels that seeks solutions by both political parties.
Keating, 73, served as Oklahoma governor from 1995 to 2003, and oversaw the state's response to the Oklahoma City federal-building bombing in 1995.