A private holding company controlled by the Rockefeller family has offered $322.1 million for Outlet Co., the broadcasting firm that owns the District's all-news WTOP-AM radio and that is planning to take over Bethesda's WHFS-FM, Outlet officials announced today.

Final details of the takeover have yet to be worked out, although indications are that Outlet officials will recommend that the board and shareholders accept the $68-a-share offer from Rockefeller Center Inc.

Within the past year, Outlet's stock had traded on the New York Stock Exchange as low as 29 1/2 a share. Today, the stock chalked up the day's biggest percentage gain on the New York Stock Exchange, jumping 11 3/4 to 62 1/2.

"The general feeling here is very positive," said Howard Kay, Outlet's director of corporate affairs, at headquarters in Providence, R.I. The deal would also have to be approved by the Federal Communications Commission.

In addition to WTOP, Outlet owns FM stations in Philadelphia, Detroit, Los Angeles and Taunton-Providence, although the Rhode Island station will be sold in a separate transaction designed to meet FCC ownership requirements. Outlet also owns television stations in Providence, Orlando, Columbus, San Antonio and Stockton-Sacramento.

Four months ago, Outlet announced plans to purchase WHFS-FM in Bethesda for $2.1 million. Company officials said then that the rock music station would be converted into a companion news station for all-news WTOP, plans that raised a small furor among WHFS listeners.

David E. Henderson, Outlet's executive vice president and president of its brodcasting division, said today that those plans remain in effect and that the station "will be operated in a complementary fashion to WTOP." There are no current RCI plans to change any of Outlet's broadcasting operations, Outlet officials said. A spokesman for RCI refused substantive comment.

Henderson suggested that during many time periods, the FM station would offer simultaneous broadcasts of WTOP's news programming, but would also offer different programming at other hours. For "competitive reasons," Henderson said he would not elaborate.

Preliminary plans are for Outlet's president, one-time Washington attorney Bruce Sundlun, to become chairman and chief executive of a new RCI subsidiary to run all the acquired stations. Henderson will become president of the venture, while Outlet's chairman, Joseph S. Sinclair, grandson of the firm's founder, will become a company consultant.

The purchase of Outlet would represent a major step in efforts by RCI to broaden its traditional real estate orientation.

In addition to Rockefeller Center and Radio City Music Hall, RCI, controlled by family trusts, owns Wessely Energy Corp. of Dallas and Cushman and Wakefield, a brokerage firm.

For several years, Outlet, which ran a profitable broadcasting business but lost money in the retail business, had sought a suitor. In 1981, Columbia Pictures proposed a purchase agreement, but when Coca-Cola Co. later purchased the movie studio Coke management decided to abandon Outlet.

Outlet reported an $18 million profit for the fiscal year ended January 1983, reversing an $18 million loss in fiscal 1982.