WASHINGTON — Rep. Alan Mollohan, a Democrat of West Virginia, whose finances are being investigated by the Federal Bureau of Investigation, is in line to take over the House panel that sets the bureau’s budget.

Mr. Mollohan, 63, is the ranking Democrat on the appropriations subcommittee overseeing the Department of Justice, which includes the FBI. His party has a long-standing practice of awarding appropriations subcommittee chairmanships to senior members, and no other Democrat has announced plans to seek the post when the party assumes control of Congress next month.

The pending appointment poses an ethical dilemma for the incoming House speaker, Rep. Nancy Pelosi, 66, who helped her party take control of Congress for the first time in 12 years by vowing to clean up a “culture of corruption” on Capitol Hill.

“If the Democrats want to be taken seriously as the party of ethics reform, then every time one of their members gets into trouble, they’re going to have to take it seriously,” the executive director of Citizens for Responsibility and Ethics in Washington, Melanie Sloan, said. Her organization is urging Mr. Mollohan to recuse himself from any decisions affecting the FBI’s budget.

A spokesman for Ms. Pelosi, a Democrat of California, didn’t respond to repeated requests for a comment. Mr. Mollohan’s office and the Justice Department declined to comment.

Earlier this year, the National Legal and Policy Center, a Falls Church, Va.-based group that backs smaller government, filed a complaint with the department questioning an increase in Mr. Mollohan’s net worth. For 2005, Mr. Mollohan and his wife reported assets worth $6.8 million to $25.7 million, up from $116,000 to $315,000 in 1999, when he restated financial disclosure forms after the group’s complaint.

In May, Mr. Mollohan told the Washington Post that the FBI had subpoenaed a Washington-based real estate company in which he had invested. In April, a nonprofit group set up under Mr. Mollohan’s leadership, the Vandalia Heritage Foundation, said in a statement that it had been told by the FBI to expect a request for information.

Fairmont, W. Va.-based Vandalia and at least three other nonprofits have benefited from “earmarks,” specific projects inserted by lawmakers into spending measures, that Mr. Mollohan secured. Mr. Mollohan, in turn, received campaign donations and gifts to his family charity from the nonprofits or their employees, according to Federal Election Commission records.

Mr. Mollohan, who hasn’t been charged with any crime, said in a June statement that his increase in net worth was a result of prudent real-estate investments.

“We received a sizable inheritance, took on considerable financial risks and had the good fortune to be investing in a rising real-estate market,” Mr. Mollohan said in the statement.

Mr. Mollohan stepped down in April from the House Ethics Committee in the wake of the investigation. He remained the ranking Democrat on the appropriations subcommittee, which also has jurisdiction over the Departments of State and Commerce.

The chairman of the National Legal and Policy Center, Ken Boehm, urged Democrats to remove Mr. Mollohan from the appropriations committee and said appointing him chairman would represent a conflict of interest.

“Somebody who is under investigation should have no leverage over those investigating him, for reasons that are blindingly obvious,” Mr. Boehm said. “You can’t have it both ways if in fact there’s going to be a serious effort to root out what’s called the ‘culture of corruption.”‘

Mr. Mollohan’s case is the third nettlesome personnel issue to face Ms. Pelosi since Democrats won control of Congress in the November 7 midterm elections. Democrats rejected her preferred candidate for the no. 2 leadership job, Rep. John Murtha of Pennsylvania, in favor of Rep. Steny Hoyer, a Democrat of Maryland, amid complaints that Mr. Murtha had used his position on the defense appropriations subcommittee to direct federal dollars to political donors.

Ms. Pelosi later considered naming Rep. Alcee Hastings of Florida, a former federal judge who had been impeached and removed from office, as head of the House Intelligence Committee. She ultimately named Silvestre Reyes of Texas to the job.