Representatives for Cerberus and Sprouts didn't respond to requests for comment. A representative for Albertsons declined to comment.
Grocery stores have been battered by food deflation over the last year, forcing them to compete more aggressively over prices. The battle has weighed on Kroger Co., the largest U.S. grocery chain. The company posted negative same-store sales, excluding fuel, for the first time in more than a decade in the fourth quarter.
Conventional grocers, including Albertsons, Kroger and Wal-Mart Stores, have expanded their offerings of organic food in response to changing consumer tastes in recent years. That's put pressure on natural grocers, including Whole Foods Market, to cut prices to better compete with the mainstream retailers.
Sprouts could fetch about $26 a share in a deal, Jefferies Group analyst Christopher Mandeville wrote in a note to clients Monday, an 18 percent premium to its last closing price. A sale may attract multiple suitors and lead to a competitive bidding process that could potentially push valuation higher, he wrote.
In September, Amin Maredia, Sprouts' chief executive officer, said deep price cuts driven by deflation were "not sustainable" and that his stores had been "exposed a little bit" by lower prices at large conventional stores.
Cerberus first invested in Albertsons in 2006, then bought another group of stores in 2013 from SuperValu. Albertsons agreed in 2014 to acquire Safeway in a deal valued at about $9.2 billion, which was completed the following year.
In 2015, Cerberus began to prepare for an initial public offering of Boise-based Albertsons, which now operates more than 2,200 stores, but delayed plans amid unfavorable market conditions.
New York-based Cerberus, led by billionaire Steve Feinberg, manages more than $30 billion in private equity holdings, distressed debt, other credit assets and real estate.