Breckinridge L. Willcox, a Washington lawyer and former Justice Department prosecutor, has been chosen by the Reagan administration as Maryland's new U.S. attorney, according to officials on Capitol Hill.

A spokeswoman for Sen Charles McC. Mathias (R-Md.) said the White House notified the senator of the long-awaited nomination Friday. No official announcement is expected until the FBI completes a background check on Willcox, a process that could take several months.

Willcox, 41, of Potomac currently works as a defense attorney in white-collar government fraud cases. He spent eight years at the Justice Department prosecuting such cases and spent two years as a special assistant to Mathias in the early 1970s. He is to replace J. Frederick Motz, who was elevated to the U.S. District Court bench during the summer.

Willcox led a list of three candidates that Mathias submitted to the White House in July. He also was in the running for the job in 1981, when Motz was selected. The White House refused to confirm yesterday that Willcox had been selected for the job, and Willcox said he had heard the news only from Mathias.

One of the primary tasks facing the state's new top federal prosecutor will be to push forward on a state-federal criminal investigation of Old Court and Merritt Commercial savings and loan associations. A spokeswoman for Mathias said the Reagan administration's delay in naming a new U.S. attorney had hampered the investigation, in part because acting U.S. Attorney Catherine Blake has not had the authority to fill vacancies on the 34-member staff.

"Obviously, it's hard to prosecute when there is no one to run [the office] and there are five vacancies," said Mathias press aide Ann Pincus.

One of the other candidates for U.S. attorney, Richard D. Bennett, 38, a Baltimore lawyer and a former assistant U.S. attorney, had strong backing from Republican Reps. Marjorie S. Holt and Helen D. Bentley. He ran the Reagan reelection campaign in Baltimore last year and made an unsuccessful bid for the state Senate in 1982.

Mathias agreed to recommend Bennett after heavy lobbying from Holt and Bentley, who saw Bennett as a rising star in the state's Republican Party. Some observers believed Bennett had a good shot at the nomination because of his strong party ties and because Mathias' planned retirement from the Senate may have lessened his influence with the White House.

The third candidate, Ty Cobb, 35, is an aggressive young deputy U.S. attorney who heads the mid-Atlantic Organized Crime Task Force.

Willcox is a partner with the firm of McKenna, Conner & Cuneo. While at the Justice Department, he prosecuted government fraud cases, including some that involved Defense Department procurements. From 1973 to 1975, Willcox worked on Maryland affairs in Mathias' office.

Willcox graduated from Yale University and Duke University law school.