Officials of Prudential Insurance Co. of America and The Washington Post Co. are conducting negotiations for the construction of a $10 million, 12-story office building on the site of the Pick-Lee Hotel at 15th and L Streets NW.

The proposed building would occupy land owned by the Washington communications firm, which would be leased to Prudential for 50 years with a 10-year renewal option. When the lease expires, the building would become Post Co. property.

According to Roger Parkinson, vice president for administration of the Post Co., negotiations "are nearly complete" with an agreement in principle already reached.

Prudential plans to begin construction in about one year with initial occupancy scheduled in early 1981. An executive of Pick Hotels Corp., in Chicago, expressed surprise when informed of the proposed office tower. Pick has a lease on the building extending through 1982 that can be cancelled before that on a year's notice.

Ralph Lewy, vice president and treasurer of Pick, said: "It's news to me." No plans have been made to close the Pick-Lee or to open another Washington hotel, he added. Pick has managed the property since 1950.

The 15th and L building is one of several major new projects planned in metropolitan Washington by Prudential Insurance and its first building downtown.

Under Prudential's Capital Real Estate Investment Office, three suburban commercial developments are in progress with a total investment of $40 million.

Prudential's projects - all in Northern Virginia - are a 15-story office at Tysons Corner, a warehouse industrial complex and the first phase of an industrial park.

Skidmore, Owings & Merrill, architects, have planned the new 15th and L building with an interior floor plan laid out at a diagonal to the exterior, rather than the conventional parallel design.

The Post Co. said it will have first call on office space in the new building and direct access to the adjacent Post building is planned on several floors. A three-story arcade will be created by recessing the first three floors and the possibility of attracting a "name" restaurant to the site is being explored. Leasing agent will be the Braedon Companies.

The Post Co. purchased the hotel building in 1964 from Pick Hotels, after which the Chicago hotel firm continued management operations under a lease agreement.

Pick Corp. had acquired the 191-room hotel property in 1950 from Tishman Realty & Construction Co. of New York, following several years of management by the Sheraton Corp.

According to the Post Co. annual report filed with the Securities and Exchange Commission, the 15th and L property has been leased through 1982 at an annual net rental of $97,500.

Adjacent to the hotel property on both sides are current properties owned by the Post Co. - a seven-story building on L Street constructed in 1950 and enlarged in 1960, with 264,000 square feet of office space; and a 258,000-square-foot building on 15th Street, completed in 1972.

The new building will have 222,000 square feet, including three levels of underground parking. Prudential will seek to attract other news-related organizations to the building but will not restrict the type of tenancy, under terms of the lease. James Farr of Farr Jewett Associates was the transaction.

The Post Co. in recent years also has purchased property in the Maryland and Virginia suburbs, for possible future construction of plants to print parts of the newspaper.

Suburban properties involved are 10 acres in Montgomery County and an 11-acre parcel in Fairfax County that is part of a 29-acre site purchased last year by a Post Co. subsidiary, Robinson Terminal Warehouse Corp.