The Los Angeles Times Mirror Co. is negotiating with RCA Corp. for purchase of Random House Inc, an RCA subsidiary.

A one-sentence statement yesterday indicated no further details, and officials in New York and Los Angeles said the statement "would have to stand" without eleboration.

"The negotiations have just begun, said Harriet Algrant, publicity director for Random House. Neither she nor Henry J. Bechtold, a staff vice president at RCA, would confirm a report of a $160 million offer.

"No figures have been put out at all," Becthold asserted. And Paul Bertness, corporate public relations director for the Times Mirror in Los Angeles, added that he "hadn't heard any figures yet."

In 1975 Random House, which includes Ballantine Books, had sales of $100 million, a figure exceeded last year. According to RCA last month, Random House had a record profit last year.

The Times Mirror publishes the Los Angeles Times and Newsday, along with other newspapers. It already has a book publishing group that includes New American Library (Signet and Mentor paperbacks), Harry N. Abrams (art books), Year Book and C.V. Mosby (medical publications), New English Library (British paperbacks), Matthew Bender & Co. (legal publications) and Southwestern Co. (educational books),

This group last year contributed revenues of $173 million out of the Times Mirror total of $976 million.

In January the Times Mirror purchased Sporting News Publishing Co., which publishes the venerable tabloid Sporting News and various sports record books. The purchase was in cash, according to the announcement, but the amount was not disclosed.

The Times Mirror also puts several special-interest magazines and owns two TV stations in Texas. It also owns a number of newsprint and wood products firms.