Finance Chairman Max Baucus says he’s looking for help from Majority Leader Harry Reid to assign a pair of plum subcommittee chairmanships that have remained vacant as other panel assignments have been snapped up.

Baucus said he was working with Reid to fill the vacancies left by former Democratic Sens. Kent Conrad of North Dakota and Jeff Bingaman of New Mexico as chairmen, respectively, of the taxation and oversight, and energy, natural resources and infrastructure subcommittees.

“The leader is trying to work that one out,” Baucus, D-Mont., said.

Charles E. Schumer of New York, the third-ranking Senate Democrat, has signaled he has no interest in either subcommittee, and other senior tax writers also appear to be taking a pass.

A Democratic senator on the committee said several factors had limited the appeal of such jobs to senior tax writers. They include questions about the role Baucus envisions for subcommittee chairmen, and Reid’s enforcement of a Senate rule that allows a full committee chairman to chair only one subcommittee on another major committee.

For now, Baucus shows little sign of changing the way the full committee divides responsibilities with subcommittees. In recent years, he has taken the lead role in the full committee on major tax bills and on other big-ticket items, potentially overshadowing the work for the subcommittees.

It’s unclear whether Reid, D-Nev., and the caucus would agree to allow waivers for senior tax writers who want to hold on to coveted subcommittee gavels on other panels instead of climbing the ladder on Finance.

Agriculture Chairwoman Debbie Stabenow of Michigan confirmed she has an interest in a swap that would allow her to succeed Bingaman as energy subcommittee chairman and hand off her chairmanship of the Social Security, pensions and family policy subcommittee. “I’m looking at it. I haven’t decided yet,” she said.

The move would give Stabenow oversight on several issues related to agriculture, including fuel taxes and ethanol tax incentives.

Jay Rockefeller of West Virginia, who plans to retire in 2014, and Ron Wyden of Oregon plan to stay put as chairmen of the health care, and international trade, customs and global competiveness subcommittees.

Bill Nelson of Florida says he might stay put as chairman of the fiscal policy subcommittee, but could look at other subcommittees on Finance. But first he wants a green light from party leaders to hold on to two subcommittee gavels, along with his new gavel as chairman of the Special Committee on Aging. He says he will not surrender his science and space subcommittee gavel on Commerce.

“I have to be chairman of the space subcommittee, so I’ve got two chairmanships,” he said.

Several other senior tax writers that chair full committees appear for now to be focused on retaining subcommittee gavels on other panels, not on Finance. Foreign Relations Chairman Robert Menendez of New Jersey also chairs a key housing, transportation and community development subcommittee on Banking. Indian Affairs Chairman Maria Cantwell of Washington chairs the coveted aviation operations, safety and security subcommittee on Commerce, a key post for her because of aircraft manufacturer Boeing Co.’s extensive operations in the Seattle area.

Homeland Security and Governmental Affairs Chairman Thomas R. Carper of Delaware also chairs the clean air and nuclear safety subcommittee on Environment and Public Works.

The logjam on Finance could open the door for a junior tax writer to grab a gavel. Benjamin L. Cardin of Maryland, who joined the panel in the last Congress, would bring long experience in the House as a former Ways and Means member to either the tax or Social Security subcommittee. His state is home to the headquarters of the Social Security Administration, which is based in Woodlawn.

Cardin chairs the water and wildlife subcommittee on Environment and Public Works and could have a choice between a Finance or a Foreign Relations subcommittee gavel.

Other potential candidates could include two newly appointed candidates, Sherrod Brown of Ohio, a former appropriator, and Michael Bennet of Colorado, chairman of the Democratic Senatorial Campaign Committee.

“We haven’t talked about it at all,” Bennet said.