What downtown Washington really needs, most District government officials agree, is another big department store.

What Bloomingdale's really wants, says Chairman Marvin Traub, is a store in downtown Washington.

But despite the intense mutual interest and direct appeals from Traub to Mayor Marion Barry, there is no Bloomingdale's in Washington now, and none is on the drawing board.

In 18 months of shopping for a downtown store, Bloomingdale's has negotiated fruitlessly with developers of half a dozen properties. They're still looking, now with the help of the District government.

Like the amorously inept pandas Ling-Ling and Sing-Sing, the District and the department store have repeatedly failed to consummate their courtship.

This inability to satisfy mutual needs is frustrating example of the difficulties the District faces in trying to shape the future of downtown.

Propelled by an all-but-insatiable demand for office space convenient to Washington's seats of power, downtown D.C. is being rebuilt faster than any other city in the country.

But the uncontrolled forces of the marketplace are threatening to cover the center city with office buildings, leaving no room for stores, theaters, restaurants, hotels and housing projects.

As a new District government study on downtown warns, "high land prices due to the expanding market for office space . . . threaten the opportunity to achieve the mix of uses necessary for a living downtown."

"A living downtown" is the goal endorsed by Mayor Marion Barry and the Metropolitan Washington Board of Trade. The mayor recently named a task force headed by National Bank of Washington President Luther Hodges Jr. to recommend specific steps needed to meet that goal.

The highest priority is rebuilding retail business, city officials stressed last month in a report that listed 11 objectives for the downtown task force.

"A first objective, strengthen the retail core, is perhaps the most important," the study said. "The retail core is literally the heart of downtown. If the retail core is healthy and active, the rest of downtown will benefit."

The core has not been healthy since 1958, when suburban shopping centers began taking business away from downtown. Three department stores went out of business -- Lansburgh's, Kann's and Jelleff's -- and retail volume dropped every year until 1977.

Sales since then have rebounded, Commerce Department reports show, with downtown department store volume climbing from $92.3 million in 1977 to $103.2 million last year.

But downtown retail sales could triple if the neighborhood achieved its maximum potential as a shopping center by adding new stores, according to a study carried out last year by graduate students at the University of Pennsylvania.

Another $200 million in retail sales would yield $12 million a year in sales tax to the District government -- far greater revenue than office buildings offer -- and would create several hundred new jobs.

Besides the high cost of land, downtown retail growth is limited by what the newest city planning study calls one of the major weaknesses of downtown -- a limited number of prime sites for new department stores in the retail core."

Bloomingdale's Chairman Traub did not need a slick study to tell him that. For a year and a half the chain has been shopping for a downtown site to complement its Maryland and Virginia stores, Traub said in a recent interview.

Unlike Saks Fifth Avenue, Nieman Marcus or I. Magnin -- whose strategies call for only a single store in markets like Washington -- the Bloomies' goal is to build at least three units and become a major factor in the department store business, Traub explained.

Originally interested in the already rebuilt section of downtown west of 15th Street NW, the New York department store recently has scouted further and further east.

Real estate specialists from Bloomies' parent corporation, Federated Department Stores of Cincinnati, have tried on half a dozen different sites. So far, everything they've looked at is too expensive, too small or taken.

Theodore Lerner, developer of the Tysons Corner and White Flint centers where Bloomingdale's has its suburban stores, is starting a major project called Washington Square at Connecticut Avenue and K Street NW, and offered the land to the department store.

Too expensive, said Traub. Even an upscale department store with extraordinary sales per square foot cannot afford to pay as much rent as a lawyer, lobbyist or trade association.

Also ruled out were the block next to Garfinckel's at 14th and G streets NW, the urban renewal properties above the Metro Center and Gallery Place subway stations and even the Willard Hotel.

Stuart Golding, the developer chosen to rebuild the Willard by the Pennsylvania Avenue Development Corp., offered three lower floors to Bloomingdale's.

Not enough room, said Traub. Bloomingdale's wants to build a downtown store comparable in size to its suburban units, with 200,000 to 250,000 square feet of retail space. For a four-floor store, that means at least 60,000 square feet of land, a vast plot by downtown standards.

The Willard also presented serious problems in accommodating both the department store and the hotel lobby on the ground floor, so that alternative has been scrapped.

Despite reservations about using even part of The Willard as a store, PADA officials encouraged Bloomingdale's to locate in the Pennsylvania Avenue redevelopment corridor, said press officer Rita Abraham.

"We think Bloomingdale's would be a great boost to what we're trying to do," she said. "We've sent them to the people we think would make a good union with them, but nothing has come of it."

Abraham said there is very little land left for a department store site in the Pennsylvania Avenue corridor, except toward the eastern end of the avenue.

Bloomingdale's isn't interested in that end of downtown, nor do city officials envision major department store development there.

The present retail core is already too elongated, planners believe. The F and G street corridors from Garfinckel's on 15th Street NW to The Hecht Co. on 6th Street NW is more than 3,000 feet long.

Half a mile is farther than shoppers are willing to walk, so the city planning department is recommending creation of a concentrated retail core that ends at 10th Street NW.

At one end would be Garfinckel's flagship store and the new building going up next to it. At the other would be the downtown store of Woodward & Lothrop, which has just undergone a multimillion-dollar renovation.

Hecht's is planning to move into the middle of that concentrated core by replacing its downtown store with a new one in the Metro Center complex planned by the Oliver T. Carr Co. The Carr project covers parts of three blocks on the north side of G Street NW extending west from 11th Street NW.

The site is owned by the Redevelopment Land Agency, the city's urban renewal arm, and is the biggest and probably most valuable tract downtown.

Because of the high land cost, Carr is planning a mixed-use project that will include several office buildings, a hotel, street-level stores and a Hecht department store with more offices above it, said Betts Able, the company's project coordinator.

Bloomingdale's has talked to the Carr Company about Metro Center but, "there's no room for another department store in there," Able said.