SAN FRANCISCO » Barnes & Noble Inc. said yesterday that online retail, media and communications conglomerate Liberty Media Corp. offered to buy the bookseller for $17 per share in cash. That amounts to about $1.02 billion, based on the number of shares it had outstanding as of March.

Barnes & Noble shares jumped more than 24 percent in extended trading after the company announced the potential deal. The offer values Barnes & Noble shares 21 percent higher than its closing price of $14.11 yesterday.

The companies haven’t yet signed an agreement, and the deal is still subject to closing conditions, including one that founding chairman Leonard Riggio keep a stake in the company and remain in a management position, Barnes & Noble said.

A Liberty Media spokeswoman could not immediately be reached for comment.

Barnes & Noble, which is based in New York and is the nation’s largest traditional bookseller, says a committee of its board will evaluate the offer.

The company put itself up for sale in August in response to pressure from billionaire activist shareholder Ron Burkle, whose Yucaipa Cos. was the majority shareholder in Aloha Airlines before the Hawaii carrier shut down on March 31, 2008.

Traditional booksellers have been facing increasing competition from online sites and discounters.

Much smaller Borders Group — based in Ann Arbor, Mich., and the nation’s second-largest bookstore chain — filed for Chapter 11 bankruptcy court protection in February. It has since been carrying out plans to closed more than one-third of its stores, and it is reportedly in talks for the purchase of some or all of the remaining stores.

Both companies have looked to online sales and to digital books and e-readers as ways to stem the steady decline in book sales in recent years.

Liberty Media operates three publicly traded companies — Liberty Interactive Inc., Liberty Starz Group and Liberty Capital Group — through which it owns stakes in home-shopping network QVC, movie channel operator Starz LLC and satellite radio company SirusXM Radio Inc.

Barnes & Noble shares rose $3.49, or 24.8 percent, to $17.60 after hours. They finished regular trading yesterday up 13 cents and traded between $8.45 and $20.45 in the past year.