American Stores Co. said its directors have authorized management to explore the sale of Acme Markets Inc., a subsidiary based in Malvern, Pa., that operates 275 supermarkets in Pennsylvania, New Jersey, Delaware, Maryland, New York and Virginia.

Acme had sales of $3.3 billion and profits of $97.1 million in fiscal 1989."While the chain is performing extremely well, the company believes the sale of Acme Markets would be in the long-term interests of American Stores and its shareholders," said J.L. Scott, chief executive officer of American Stores.

Scott said the proceeds from the possible sale would be used to reduce debt, allowing American to focus its time, energy and capital resources on its food and drugstore operations "in other profitable and growing markets."

He said the sale would be made only if directors determined the price and other terms of the sale were satisfactory.

The company said that with lower debt levels from the possible sale of Acme, American would pursue aggressive investments in technology, remodeling and new store programs in remaining markets.

Lehman Brothers, which has been retained to act as the exclusive agent in soliciting bids for Acme, has indicated there are a number of parties that may be interested in the chain.