Some of Mayor Walter E. Washington's political rivals think it's an interesting coincidence that Joseph P. Yeldell's new office in the National Theater Building is only a few doors from Bassin's Restaurant. It was in the office space upstairs over Bassin's that the Mayor's 1974 campaign organization had its headquarters.

When the Washington foes scan the roster of Yeldell's staff and analyze Yeldell's new responsibilities as general assistant to the Mayor, some are willing to wager that Yeldell is gearing up to run the Mayor's Campaign '78.

That suggestion brought only laughter from Yeldell when a mayoral spokesman asked him to respond to a reporter's question. Yeldell's job assignment, the spokesman said, is simply, "Whatever we ask him to do."

The former director of the Department of Human Resources (DHR) moved into the new third floor quarters just last week. The city is renting the facility for $16,500 a year because there was no adequate space for Yeldell in the District Building. While awaiting completion of remodeling of the new office, Yeldell operated out of his old office in the DHR headquarters.

The new facility is a suite of half a dozen offices, including Yeldell's, with white-an-gold walls. Yeldell has a staff of six, including his long-timer secretary Lillian Manson.

Two persons with ties to the Mayor in previous campaigns are working with Yeldell. Herbert Barksdale has been detailed from DHR to help Yeldell coordinate relations with the city's and Carol Payne, also has been detailed from DHR to work with the city's minority contracting effort.

Barksdale was a major staff person in the Mayor's campaign office in 1974 and Payne was the Mayor's scheduler. The fact that they're on Yeldell's staff, said spokesman Sam Eastman, is only "coincidental." Soon to join the staff Eastman said, is Sam Jordan, the Mayor's principal community troubleshooter.

What Yeldell is actually doing, in addition to building a liason with ANCs and helping determine which minority contractors will get a share of the city's business, is overseeing the operations of the Office on Aging and completing a report on whether the city should establish a job corps program.

None of that is overtly political. But much of it could be important in any attempt by the Mayor to put together a campaign organization should he decide to run again in 1978.

Thus it appears that if there is a future role for Yeldell in the Mayor's administration it will be as Mr. Outside, the administration's point man with the Washington community. That depends, of course, on whether the Mayor decides to run again.

Here's what Stuart Rosenblatt, director of the Washington office of the U. S. Labor Party, believes is the real reason there is an effort afoot to get the Mayor out of City Hall and into the State Department as an ambassador. Read it slowly. It's very heavy:

The push to get the Mayor to Foggy Bottom, Rosenblatt says, is being coordinated by the White House, "specifically unders its wing that connects to mission, he notes, was set up by David Rockefeller, chairman of the board of Chase-Manhattan Bank, and many of its members are important in the Carter White House.

The reason they want to oust the Mayor, Rosenblatt asserts, is because Mayor Washington stands for a "high standard of living" among the people served by government, which means more city services and fewer budget cuts.

The trilateralists want to cut the municipal budget because they need the extra money to bail out Chase, says Rosenblatt, predicting that the huge bank will go bankrupt "on Sept. 15, Sept. 18 at the latest."

"The idea is that they want urban based political machines out of existence," Rosenblatt says. "Any major or state representative who stans for a high standard of living or at least would be against massive service cuts is susceptible to the kind of economic and political warfare now going on."

But, a reporter asks, why can't a job be found for the Mayor. That's simple, comes Rosenblatt's reply. It's merely a move to intimidate the Mayor into going along with the budget cuts. "The way these guys work is that they threaten you with what they'd like you to do and they do that to try to get you to fall into line."