D.C. Del Walter Fauntroy plans to give up the chairmanship of the House District subcomittee that overseas the city's budget and home rule in favor of the chairmanship of the House Banking subcommittee on domestic monetary policy.

The move by Fauntroy, the city's only official link to Capitol Hill, comes at a time when the District is in serious financial trouble. Fauntroy would remain a member of both the House District Committee and its government affairs and budget subcommittee, but under House rules he cannot hold two subcommittee chairmanships.

Fauntroy's press secretary, Eldridge Spearman, said Fauntroy has "indicated and expressed an interest" in the Banking subcommittee. Spearman said the Banking subcommittee "is very important, considering the country's economic climate." He said that having Fauntroy as chairman would "help him influence financial decisions." Another Capital Hill aide, however, described the subcommittee as a "nothing committee."

"All the actions he takes in regard to Capitol Hill are in the best interest of the people of the District of Columbia," Spearman said. Fauntroy was out of town yesterday and unavailable for comment. Spearman said Fauntroy would explain to his constituents later why he wanted to relinquish the District subcommittee chairmanship and how he plans to represent their interests.

Fauntroy was once considered the most popular political figure in District politics but he has been said to be frustrated at not being closer to the power and prestige of the city's operations. The chairmanship of the Banking subcommittee could give Fauntroy greater national political exposure by providing an opportunity to oppose President-elect Reagan's economic policies in favor of full empolyment and other traditional, New Deal-style Democratic legislation, sources said.

Although Fauntroy worked with civil rights activists Jesse Jackson and Andrew Young in the early 1960s, he never attained their national and international status. Fauntroy's most recent attempt at international politics involved meetings in 1979 with Palestine Liberation Organization chief Yassar Arafat.

Spearman added later that as chairman of the banking subcommittee Fauntroy could help push through parts of Mayor Marion Barry's financial programs for the city. The House District subcommittee can hold hearings on the city's budget, but the budget must be approved by the House Appropriations Committee.

Not being chairman of the District subcommittee "doesn't negate his authority" on the subcommittee or full committee, Spearman said. "He is going to exercise influence on behalf of the District of Columbia, whether he's chairman of the District subcommittee or not, because of his seniority on that committee," Spearman continued.

The vote for the Banking subcommittee chairmanship is expected next week. Fauntroy's main challenger for the spot is Rep. Stephen L. Neal (D-N.C.). Congressional sources said yesterday they believed Fauntroy already had lined up enough support for the chairmanship.

"I would like to be chairman of that [subcommittee]," Neal said. The subcommitte is important because it overseas inflation rates and employment, he said. Because Fauntroy has more senority on the Banking committee, "he can exercise that claim" to the subcommittee chairmaship, Neal said. But, he added, "Maybe he would like to do something else."