"Aspects of Twentieth-Century Art," on view through September at the National Gallery of Art, is a tantalizing show.While surveying the past, it offers us a glimpse at the new East Building's future.

The borrowed objects in it area about to be reclaimed by their private leaders. But if all goes well - and that is a big if - they someday may return to Washington for good.

The viewer who sees "Aspects" should look closely not only at the names of Mondrian, Matisse, Boccioni, Picasso and others, but also at the other names in smaller type below. Malbin, for example, Neumann and Tremaine, Whitney, Hemingway and Mellon. These names are repeated throughout the "Aspects" exhibition, and all of them belong to American collectors who, as Carter Brown delicately puts it, have "shown a special interest in the National Gallery of Art."

These extraordinary objects - the Whitney Fauves, the Malbin Futurists - are beautiful and rare. They also are available.

Their presence at the Gallery reflects a tense, ongoing courtship. They have not been pledged or promised, but with maximum politeness, and with the fervent crossing of curatorial fingers, they all are being eyed for eventual inclusion in the permanent collection of the new building on the Mall.

That is, after all, one reason it was built.

Paul Mellon and his family, who paid $94.5 million for the East Building's construction, do not intend to stock it. Instead they expect other generous collectors to fill it up with art.

The tax laws, which encourage the migration of privately held objects into public hands, are working in their favor. "Victory Boogie Woogie," the Tremaine Mondrian; "Boy with Pipe," the Whitney's ravishing 1905 Picasso; Joan Miro's "The Farm," which belonged to Ernest Hemingway; and the other objects shown probably will go to some art museum. The question is which museum, and the competition is extremely stiff.

Consider, for example, the superb collection of Italian Futurism owned by Lydia Kahn Winston Malbin, who once lived in Detroit. "Lydia, Lydia, Wilt Thou Forsake Detroit," cried that city's Free Press when Malbin and her art moved to Manhattan in 1974. "Detroit looks like a jilted lover," the newspaper complained.

Malbin, the daughter of architect Albert Kahn, has assembled a collection of Ballas, Severini and Boccionis that would be the envy of any museum. She has stored them at the Guggenheim and shown them in Detroit. Though they would fill a gap in the Gallery's collection, and though its curators are hoping, it is far from certain that these objects will come here.

John Hay Whitney, too, has established close relations with other art museums. But luckily the Whitney Museum in Manhattan collects American art only, and Whitney's Fauves, his Braque, and his beautiful Picasso all were done in Europe. And it is not insignificant that Whitney is vice-president of the National Gallery of Art.

Paul Mellon, too, supports more than one museum. His finest English pictures already have been given to the gallery he built for Yale University. But the eight works he has lent to the "Aspects" exhibition, one of them a wonderful 1899 self-portrait by Picasso, would better fit the National Gallery's collection.

Mr. and Mrs. Burton Tremaine of Meriden, Conn., whose loans now on display include that late and vibrant Mondrian, have been generous to the National Gallery in the past.

Other lenders to the show include Mr. and Mrs. Andrew S. Keck, who have lent their Matisse silkscreens; Mr. and Mrs. Robert B. Eicholz, who are represented by a 1911 Braque; and Mr. and Mrs. J. V. Mladek, who have lent a Kupka. They all live in this city.

Though the Gallery is in their debt, there is a subtle quid pro quo attached to such loans. Though the market value of the borrowed works on view may be well established, the price tags on these objects, or the allowable deductions flowing from their gifts, have not been diminished by their presence in a loan show at the National Gallery of Art.

And neither has their fame. "Capriccio in February," the large, impressive Paul Klee lent by Mr. and Mrs. Morton G. Neumann of Chicago, has never been as famous, or as often reproduced, as the smaller Klees on paper in, say, the Phillips Collection. The "Capriccio" was a masterwork before it came to Washington, but now it is a masterwork that has been reproduced in color, and one that a million viewers have had a chance to see.

The "Aspects" exhibition is really many shows in one. It includes a survey of "Picasso and Cubism"; a small Fauve exhibit, largely provided by the Whitneys; the Malbin Futurist exhibit; and a room of Giacomettis, all gifts from Enid Haupt. The majority of works in the East Building are only there on loan. The Dresden show, for insteance, will close on Labor Day and is not likely to return.

But the new East Building was not built only for loans. "As the Gallery's survey . . . grows to include samples from the 20th and later centures," writes Carter Brown, "the East Building will be a logical place to exhibit them." The "Aspects" exhibition with its tantalizing loans suggests the future that is in store for the new museum on the Mall.