The retail giant was among those that analysts said could potentially make a counter bid for the grocery chain as the company has been focusing its deal making on bulking up its digital business.
A Wal-Mart spokesman 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.
Although Wal-Mart's name had been mentioned as a rival suitor, some felt expected that the deep-pocketed Amazon would have countered any offer with a sweeter bid.
Whole Foods shares have been trading above Amazon's $42 bid since the deal was announced last Friday, as stock market investors have speculated about the possibility of a higher offer.
Shares of Whole Foods and Walmart both remained unchanged in aftermarket trading Friday.
JAB Holdings was also been flagged as a potential bidder for Whole Foods by retail analysts. The private equity player has been shifting its focus to restaurants and food and beverage businesses, most recently it said it would purchase Panera Bread in a deal valued at about $7.5 billion.
Whole Foods has been under pressure from activist investor Jana Partners and money manager Neuberger Berman, which have called on Whole Foods to sell itself. The investors have criticized Whole Foods for its poor performance and have suggested the chain could be merged with another grocer.
— Reuters contributed to this report