The acquisition talk began when financial website Briefing.com reported Thursday about "hearing chatter that privately held Publix is interested in" Whole Foods. Officials with both Whole Foods and Lakeland, Fla.-based Publix declined to comment on the reports, saying they don't discuss rumors.
Whole Foods is one of Austin's highest-profile companies, with about 2,800 employees in Central Texas and 84,000 companywide.
Whole Foods' shares have risen almost 7 percent since the acquisition reports hit the street on Thursday, closing Friday at $40.93, the stock's highest level on the Nasdaq exchange since early May.
During the two-day period, 28 million shares traded hands, more than double the average volume for Whole Foods.
"The stock has rallied substantially in two days," said Brian Yarbrough, an analyst for Edward Jones. "Someone believes there is some truth to this rumor."
Whole Foods stock has slumped since it on May 6 reported earnings that fell short of Wall Street expectations, sending share prices below $40. The stock hadn't been at that level since February of 2012.
An acquisition would be a dramatic twist in the Whole Foods story, as executives say the company has been in serious growth mode with plans to grow from 383 stores today to 1,200 locations eventually.
"We are not even a one-third of that yet," Yarbrough said. "I would have to think they have no interest if they really believe this industry can be as big as they think. If they really believe in the growth story, they are probably not willing to pull away."
Publix is a privately held chain founded in 1930 that has seen tremendous growth in recent years, reaching 1,077 stores. About 750 of those locations in Florida. The rest are spread out across five nearby states.
Whole Foods has 20 stores in Florida and overlaps with Publix in at least one other market in Georgia.
The employee-owned grocery chain is the country's fifth-largest food retailer, and although privately held, it does have stock and publishes financial reports through the U.S. Securities and Exchange Commission, Ken Goldman, analyst at J.P. Morgan, said in an analysis of the two chains.
Publix is valued at $24.1 billion, while Whole Foods is at $13.9 billion, Goldman said.
Acquiring Whole Foods, analysts said, would give Publix an entry into the natural foods sector that Whole Foods has helped make mainstream.
"I do think it's doable; it makes sense if you want to grow natural and organics," Yarbrough said.
Meanwhile, Whole Foods leadership might not be in a position to block a takeover due to limited insider ownership, Yarbrough said. Whole Foods co-founder and co-CEO John Mackey owns less than 1 percent of the company's stock, while the management team combined may own less than 5 percent, Yarbrough said.
"They don't own enough to block it," he said.
However, it's unclear if Publix would push for a hostile takeover bid, he said.