U.S. Sen. Joseph Lieberman, the Democrat-turned-Independent, hinted at an Independent reelection bid during a visit to the House of Bread in Hartford Tuesday.

Lieberman, who is up for reelection in 2012, said he still hasn’t decided whether he’s going to run again. And, he said, if he does run how exactly he would go about doing it is still up in the air.

He’s still a registered Democrat and caucuses with Democratic Senators in Washington, but he supported Republican U.S. Sen. John McCain’s presidential bid in 2008 and has stepped across the aisle to support Republican legislation on occasion. Also the Connecticut for Lieberman Party he created in 2006 is no longer there as a vehicle since it was co-opted by his opponents, who failed to garner one percent of the vote this November.

“I’ve enjoyed being an Independent, but I want to at least look at the other two possibilities,” Lieberman said referring to the two major parties. “I’ve enjoyed being an Independent so I guess that’s the most natural way to run, but I haven’t decided.”

“I don’t meet all the requirements of either party,” Lieberman admitted. “And today both parties are really imposing requirements more than when I got started in politics.”

He said as he makes his decision he will have to answer some tough questions.

“One do I want to continue to do that or do I want to try something else in my life. Two obviously can I contribute something to my state and my country,“ Lieberman said. In answering the second question Lieberman said he thinks as an Independent he has a role to play in putting “majorities together to get things done.”

Looking back on the 111th Congress Lieberman said he played an important role in getting the Economy Recovery package and the health care reform legislation passed.

“I ended up being there as an Independent at the end bringing about the 60 votes necessary to pass those two things,“ he said. “So I think that’s going to be more true not just for be, but for anybody whose able to step away from party orthodoxy in either party cause it’s going to be harder to get to 60 when you’ve only got 53 members that are part of the Democratic caucus.”

If Lieberman does decide to run it’s looking like it will be a three-way race.

Republican Linda McMahon, who lost to U.S. Senator-elect Richard Blumenthal on Nov. 2, told WFSB’s Dennis House on Sunday that she hasn’t ruled out anything.

“I’m not taking anything off the table,” McMahon said repeatedly.

Edward Kennedy Jr. and U.S. Rep. Chris Murphy have been mentioned as possible Democratic opponents to Lieberman.