Mayor Marion Barry has asked former City Council chairman Sterling Tucker to accept appointment as chairman of the troubled D.C. Board of Elections and Ethics, according to city government sources.

The sources said Barry might announce his choice to replace outgoing board chairman Albert J. Beveridge III as early as today. The three-year appointment, which would pay a maximum of $26,500 annually, is subject to confirmation by the City Council.

Barry confirmed through his press secretary that Tucker, who narrowly lost the mayoral nomination to Barry in 1978 and was defeated in a bid to regain his old job as council chairman last year, is "under consideration for the post," but declined further comment.

If nominated and confirmed, Tucker, 58, would be one of two new appointments Barry is expected to make to the three-member board, which oversees the city's voter registration, certifies candidates and conducts elections. In addition, the board hears cases brought by the Office of Campaign Finance involving the city's ethics laws.

In recent years, the board has been plagued with problems involving the city's voter registration lists and the conduct of elections. Last September, more than 20,000 voters, one-fifth the turnout, were forced to cast special ballots when their names did not appear on registration lists. Officials later determined that all but a few hundred were properly registered.

Elections officials have said that the city's voter rolls, with more than 370,000 names, are riddled with duplications, errors and persons who have either moved from the city or died.

The board has proposed that all of the city's scheduled elections this year for school board posts and Advisory Neighborhood Commission members be postponed until 1984 to give the elections office time to reorganize and clean up its records. Those proposals are pending before the City Council.

Tucker, a former head of the Washington Urban League, served on the appointed City Council and was the city's first elected chairman of the council, giving up the post in 1978 to run for mayor. Tucker was succeeded by Arrington Dixon, a former Ward 4 council member, who lost his reelection bid to Clarke in last September's Democratic primary.

Meanwhile yesterday, Dixon, who left office Jan. 2, announced that he will become a vice president of Planning Research Corp. Computer Systems, part of an international computer company with offices in McLean that does much of its work with the Defense Department.