By Catharine Richert, CQ Staff

Sen. Joseph I. Lieberman wants to stay in the Democratic caucus, but not give up his plum chairmanship of the Homeland Security and Government Affairs Committee as some Democrats want, an aide to the senator said Friday.

In a closed-door meeting Thursday, Senate Majority Leader Harry Reid , D-Nev., asked the Democrat-turned-Independent to give up his gavel for “a lesser committee,” according to the Lieberman aide.

Democratic leaders have been mulling a way to punish Lieberman for campaigning against President-elect Barack Obama on the campaign trail. Lieberman stumped for Republican Sen. John McCain of Arizona instead.

A Democratic aide said party leaders are considering allowing a secret caucus vote to decide Lieberman’s fate at a meeting the week of Nov. 17. The vote would take the pressure off Reid, a man Lieberman has long called a friend, the aide said.

Republicans meanwhile have publicly encouraged Lieberman to join their caucus, but it’s unclear whether they have anything to offer that he might want.

Lieberman became an independent in 2006, but has continued to caucus and vote with Democrats on all issues except the war in Iraq.

“He said, ‘Look. I’ve been a loyal vote’,” Lieberman’s aide said, recounting what happened at the meeting. “His preference is to stay in the caucus. Both men agreed that they want to work this out.”

There are few alternative chairmanships available. According to Senate seniority, Lieberman could switch places with Sen. Daniel K. Akaka , D-Hawaii, and become chairman of the Veterans’ Affairs Committee.

Or, if Sen. John Kerry , D-Mass., takes over from Vice President-elect Joseph R. Biden Jr. , D-Del., at the Foreign Affairs Committee, his spot on the Small Business and Entrepreneurship Committee would become vacant.

Democratic leadership aides said previously that Lieberman would be offered a subcommittee chairmanship, but that option was not discussed in the meeting, according to the Lieberman aide.

Including his colleague from Connecticut, Sen. Christopher J. Dodd , Lieberman has reached out to at least a few Democrats, his aide said. It’s unclear if he will continue to canvass members of his former party for support.

Meanwhile, Minority Leader Mitch McConnell , R-Ky., recently spoke with Lieberman over the phone, but a McConnell aide could not classify the content of the conversation.

There are few ranking memberships that the GOP could offer Lieberman, and incumbents may not be keen on stepping aside to allow someone who has voted with Democrats on every issue except the war, take their spot.