The decision by Rep. Michael Barnes (D-Md.) to run for the U.S. Senate has touched off a scramble among Montgomery County Democrats who are thinking of running for his seat, and at least one Republican is likely to enter the race.

The potential contenders on the Democratic side include a wealthy state senator and business executive, a former U.S. Senate aide and a previously unsuccessful candidate for the 8th District congressional seat, which Barnes won in 1978 after 20 years of GOP control.

State Del. Constance A. Morella, a Bethesda Republican who has previously received wide bipartisan support, said she will declare her candidacy after Barnes' formal announcement of his plans. "This is something I've always wanted to do and the opportunity has presented itself," she said.

State Sen. Stewart Bainum Jr. a wealthy motel and nursing home executive who is known for his effort to end tax breaks to male-only private clubs, professed interest in the race and said, "I'm moving in that direction."

Democrat Victor Crawford, a Rockville lawyer who served in the state Senate for 16 years, said: "I'm thinking about it very seriously. I figure the field's wide open. Right now there are no front-runners. Why not?"

Leon G. Billings, former staff director for the U.S. Senate subcommittee on environmental pollution, said he will run but will make no formal announcement before Barnes makes his formal declaration next Monday for the Senate seat being vacated by Charles McC. Mathias (R-Md.).

Democratic National Committeman Lanny Davis, a lawyer and lobbyist who narrowly lost his bid for the seat in 1976, said recently he is considering running for Barnes' seat, as is Wendell Holloway, a Ford executive who is the only black so far to express an interest.

Others mentioned by political observers as possible Democratic candidates are County Council members David Scull and Esther Gelman and state Dels. Lucy Maurer and Marilyn Goldwater, although they are said to be more interested in other offices.

Acknowledging the uncertainty surrounding the race more than a year before the election, Democratic activist Gil Lessenco nevertheless identified Bainum as the early favorite.

"He comes out of the heartland of Montgomery County, the Silver Spring-Takoma Park area, and he has a substantial ability to gather resources," Lessenco said. "But I also think Wendell Holloway could prove to be a surprising factor, particularly with several candidates in the race. I think Leon Billings is extremely capable," but handicapped by having held no previous elective office.

Several potential candidates agreed Bainum would probably hold the fund-raising edge. But Billings, a former fund-raiser for the Democratic Senatorial Campaign Committee, said, "I wouldn't consider it if I thought that was the only requirement. I think the people in Montgomery County are too sophisticated for that."

Montgomery voters register Democratic by a ratio of more than 2 to 1 but have a history of choosing candidates without regard for party affiliation.