Lieberman's affiliation with Democrats is up in the air. Senate Majority Leader Harry Reid of Nevada, angered by Lieberman's support of Republican John McCain for president, is considering yanking Lieberman's chairmanship of the Senate Homeland Security and Governmental Affairs Committee as punishment.
Lieberman and Reid met Thursday to discuss Lieberman's options, including possible committee and subcommittee posts for him. Those talks are ongoing.
A Lieberman aide, who requested anonymity because the talks are confidential, said Friday that Lieberman and McConnell, R-Ky., have spoken in recent days about the possibility of Lieberman joining the GOP conference. McConnell spokesman Don Stewart would only confirm that the two men have had recent discussions.
Lieberman was Democrat Al Gore's vice presidential running mate eight years ago. He became an independent after he failed to win the Democratic Senate primary in Connecticut in 2006. Lieberman won the general election as an independent but is still registered as a Democrat.
Although he caucuses with Senate Democrats, Lieberman angered Democrats by criticizing Barack Obama during the presidential race.
Since 2006, Democrats had tolerated Lieberman's political straddling because he gave them a 51-49 majority by being part of their caucus. With Democrats tightening their hold on the Senate to at least 55 seats in Tuesday's election, Lieberman no longer plays that role.
Lieberman aligned himself with McCain and President Bush on the war in Iraq but tended to vote with Democrats on most domestic issues.