The long-vacant Willard Hotel may prove to be the most popular white elephant Washington has ever seen.

The Pennsylvania Avenue Development Corp. will open bids July 28 from developers who want a chance to renovate the old structure, and build on the land between it and the nearby Washington Hotel.

So far PADC has sold 177 sets of the plans needed to prepare a proposal for the project. That response boggles the minds of PADC officials, who breathed a sigh of relief when developer Oliver Carr first offered to consider the project.

The only firm besides Carr that publicly has expressed interest in the Willard is the Radisson Hotel Corp. of Minneapolis, which has rejuvenated several old downtown hotels in other cities.

Minneapolis millionaire Curt Carlson bought the aging Radisson Hotel in that city a decade ago, turned it around and began building what is now a 20-unit hotel chain. The Muehlebach in Kansas City - headquarters for the Republican convention in 1976 - was rescued from the rats by Radisson, which recently reopened The Cadillac in downtown Detroit.

Both Radisson and Carr are likely to have partners on the Willard project: Carr is a builder, not a hotelier, and Radisson generally renovates and runs buildings owned by other investors.

Other major developers are expected to show their hands when proposals are opened by PADC. The choice will be based on competitive bids reflecting not only the price the developers are willing to pay for the property, but also the relative merits of their proposals.

In the interests of historic preservation, the Willard's shell will have to be retained, but developers will have a free hand inside. As a safety valve. PADC has provided that the Willard could be rebuilt for offices. But a hotel is the preferred use and is almost certain to be built if the convention center is approved.

The properties between the Willard and neighboring Washington Hotel will be offered with the hotel: PADC officials expect most bidders to want the extra land which could be used for parking garages, shopping or an addition to the hotel.

Once a developer is selected, it probably will take 18 months to plan the renovation job, which could be completed by 1981 or 1982.