The Phoenix-based company has chosen Goldman Sachs Group Inc and Credit Suisse AG to lead a proposed offering, the sources said.
Goldman Sachs and Credit Suisse declined to comment. Apollo and Sprouts could not be reached for immediate comment.
The people asked not to be named because the matter is not public.
Sprouts was originally a family-owned chain which traces its roots back to a fruit stand founded in 1943. The company now operates more than 150 stores in Arizona, California, Colorado, New Mexico, Nevada, Oklahoma, Texas and Utah.
Sprouts was acquired by Apollo in 2011 and was later merged with Henry's Farmers Market, another Apollo holding. Last year, Sprouts was merged again with grocer Sunflower Farmers Market.
Sprouts generates roughly $2 billion in annual revenue, according to several media reports.
The company is trying to come to market amid strong share performances from other high end grocers like Whole Foods Market Inc and Fresh Market Inc.
Shares of Fairway Group Holdings Corp also surged more than 30 percent after the grocery chain's IPO last week in which it raised $178.1 million.