The owners of The National Enquirer have been in talks to sell the tabloid to Ronald W. Burkle, a supermarket magnate with ties to President Bill Clinton, according to three people with direct knowledge of the negotiations.

While representatives of The Enquirer, which is owned by American Media Inc., have been in negotiations with Mr. Burkle’s team, the deal could fall apart, said the people, who spoke on the condition of anonymity to describe private negotiations.

Mr. Burkle, who specializes in buying distressed companies, made his initial fortune buying and selling supermarkets in California. In 1999, he helped buy the Pittsburgh Penguins hockey franchise out of bankruptcy; the team has won three Stanley Cup championships since then. In recent years, Mr. Burkle has been a regular in the gossip pages and on the A-list benefit and party circuit, hobnobbing with the likes of Madonna, U2, Sean Combs, Leonardo DiCaprio and Sarah Ferguson, the Duchess of York.

Mr. Burkle and his private equity firm, Yucaipa Companies, did not initially respond to requests for comment. After news of the talks was reported by The New York Times on Thursday, a representative said Mr. Burkle and Yucaipa were not interested in The Enquirer. “Ron Burkle and Yucaipa are not buying The Enquirer,” Frank Quintero, who works at the firm, said in an email. “Furthermore, I’m told we are not in talks to buy it.”