Activist investor Jana Partners has accumulated an 8.8 percent stake in Whole Foods and wants the organic market to explore a possible sale, according to a Monday regulatory filing. The hedge fund, founded by Barry Rosenstein, is putting more pressure on the grocer's management to turn around slow growth.

Jana, along with several allies, wants Whole Foods to better operations and technology, shake up the board, and research how much possible bidders might be willing to pay. This comes as Whole Foods struggles to morph into a national chain and maintain the rapid growth it previously experienced.

The upscale market's stock lost almost half its value since peaking in 2013 and same-store sales have fallen over the last 18 months, according to The Wall Street Journal. Some investors said while the company was taking the appropriate steps, it was moving too slowly.

John Mackey, the CEO and co-founder of Whole Foods, has been under pressure to get things in order quickly. But until the end of last year, he shared the CEO role with Walter Robb. While Mackey was able to rejuvenate the business once before, it still remains unclear whether or not he can turn things around again.

"I'm tremendously proud of the impact that my company has had, both in increasing cultural awareness of food and in offering millions of American more options when it comes to making health, sustainable food choices," he wrote in his new book, The Whole Foods Diet, released on Tuesday.