Fresh Market Inc.’s founder and chairman, Ray Berry, is working with Apollo Global Management LLC to explore a possible buyout of the grocery chain, according to a person with knowledge of the matter.

Berry turned to Apollo after seeing how it handled the acquisition -- and subsequent initial public offering -- of Sprouts Farmers Market Inc., according to the person, who asked not to be identified because the deliberations are private. Apollo didn’t immediately respond to a request for comment, while Fresh Market declined to comment.

“It isn’t a high-growth company, but it has predictable cash flow that will support some leverage,” said Erik Gordon, a business professor at the University of Michigan. “Apollo knows how to handle companies like this.”

Fresh Market shares jumped 7.8 percent on Friday after Reuters first reported on the discussions, saying that Berry was also seeking support from additional private-equity firms. Berry, who owns 4.1 percent of the company, also may team up on a deal with son-in-law Michael Barry, who has a 6.4 percent stake, Reuters said. No offer has been made, and a deal may not come together.

The stock rose to $26.19 in New York, the biggest one-day gain in more than a year. Shares of the Greensboro, North Carolina-based company had been down 41 percent this year through Thursday’s close.

The discussions cap a turbulent week for the supermarket industry. Albertsons Cos. delayed its IPO on Wednesday, and Wal-Mart Stores Inc. suffered its worst one-day stock decline in 27 years after warning of a profit decline.

Since going public in 2010, Fresh Market has seen its sales growth slow, hurt by mounting competition. The company was founded in 1982.

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