Whole Foods, which accepted a $13.7 billion offer from Amazon.com Inc (AMZN.O) last week, has not received any rival bids as of Friday, a second source said. Both sources spoke on condition of anonymity because the matter is confidential.
Wal-Mart spokesman Greg Hitt declined to comment on whether the company is considering a bid for Whole Foods. Whole Foods and Amazon did not immediately respond to requests for comment.
Whole Foods shares have been trading above Amazon's deal price of $42 per share since the deal was announced last Friday, as stock market investors speculate about the possibility of a higher offer.
Whole Foods shares reached a high of $43.84 earlier on Friday, but dropped after Reuters reported that no rival bids have so far emerged. Its shares were last trading after hours at $42.85.
Wal-Mart had been tipped as a potential bidder for Whole Foods by retail analysts, although Hitt previously called reports that Wal-Mart might put in a rival offer "false and baseless."
Wal-Mart, the world's largest retailer, has been investing heavily in building its e-commerce business and has been acquiring smaller online companies such as Jet.com, ModCloth, Moosejaw and Bonobos.
"Bidding for Whole Foods would be a 180-degree turn from what Wal-Mart’s strategy has been for the past two to three years," said Edwards Jones analyst Brian Yarbrough.
Amazon's proposed purchase of Whole Foods brings disruption to the $700 billion U.S. grocery sector, a traditional area of retailing that is in the middle of an intense price war.
In preparation for that price war, Wal-Mart in recent months has cut grocery prices, improved its fresh food and meat offerings, modernized shelving and lighting in its grocery department and expanded its online pick-up service.
Both Amazon and Whole Foods cater to younger consumers, including millennials, as well as more affluent shoppers.
Whole Foods has said it will continue to operate stores under the Whole Foods Market brand, and that John Mackey will remain chief executive.
Reporting by Nandita Bose in Chicago and Greg Roumeliotis in New York; Editing by Bill Rigby