Sterling Tucker, the former D.C. City Council chairman narrowly defeated in his 1978 bid to become mayor, has begun an intensive effort to line up potential support for another run for mayor in 1982.

In a succession of luncheon meetings and private conversations with local business and political leaders, Tucker has given the clear impression that he intends to run, sources said. He has also held a number of informal strategy sessions with close friends, though he denies that this represents an attempt to develop a new campaign organization.

Currently serving out his last few lame-duck days as a Carter administration assistant secretary of Housing and Urban Development, Tucker freely acknowledges that he is "testing the waters" for another mayor's race but denies that any firm decision has been made. He says that when he leaves the government in January, he plans to do consulting work, which will "still leave me a lot of time for public service."

Tucker said he will not run without some measurable indication of widespread popular support.

Several persons who have talked with Tucker about his ambitions agree that he acts and sounds like a man who still wants very much to be mayor. "He hasn't gotten it out of his system," said one. "He still hasn't reached the level he feels he ought to reach."

"Sterling called me for lunch the other day," said a politically active busines leader who, like most other sources, asked not be identified. "He kept saying he's trying to decide whether to run. But in my view, the decision has already been made to go."

According to sources who have discussed campaign strategy with Tucker at a series of informal meetings, Tucker believes he has a base of support among blacks who gave him and former Mayor Walter E. Washington a total of nearly two-thirds of the vote in the 1978 Democratic primary election.

The sources said that Tucker also believs Mayor Marion Barry's support among business leaders, public employe unons and predominantly white neighborhoods has eroded.

Barry's administration "came in with a great deal of promise, but never had a chance to get off the ground," Tucker said. The city's budget crisis, he said, has diverted Barry's attention from such problems as housing and the quality of the public schools.

"One gets the impression that the city is flying by the seat of its pants," Tucker said. "I suppose Marion knows as well as anyone else that people feel his is a troubled adminstration."

It is conceivable, however, that Tucker would have political liabilities of his own. He has been absent from the fast-shifting local political scene for two years, and holds no elective office from which to campaign. The 1982 Democratic mayoral primary will probably differ sharply from the 1978 contest, in which three extremely well-known officials competed and finished in a virtual dead heat.

Moreover, Tucker's personal finances and those of hise 1978 campaign have come under close scrutiny, and other candidates would undoubtedly seek to remind voters of questions that were raised.

Sources close to Tucker describe him as having been stunned by his 1978 loss to Barry. Tucker had believed in the days before the election that he was leading both Barry and Washington -- a perception shared at the time by most local observers.

He reportedly told friends and associates just days after that defeat that he wanted to try again in 1982, and began to raise the issue again this fall.

Within the last month, Tucker has met with a number of influential local businessmen. National Savings and Loan Trust Co. President Joseph H. Riley described a recent conservation with Tucker as merely a chance to reestablish contact after Tucker's absence from the city government, while other business leaders, who asked that their names not be used, described explicit request for financial and political support in the event that Tucker finally decides to run.

In addition, Tucker has been buttonholing political leaders -- including several members of the City Council and the D.C. Democratic State Committee -- to explore the possibilities for support and to try to guage the level of Barry's current popularity.

Barry has already taken actions, such s marshaling his 1978 precinct workers, indicating that he is preparing for a reelection bid.

A host of other local Democrats -- City Council Chairman Arrington Dixon, Council members John L. Ray and Betty Ann Kane and 1974 mayoral candidate Clifford Alexander, for instance -- also are reported to have ambitions to run against Barry in 1982, and thus have refused to agree to support Tucker or anyone else. Dixon, Ray and Kane all echoed Tucker's statement that they are keeping their options open.