A deal for roughly $400 million, part of Hostess Brands Inc's bankruptcy process, could be announced as soon as Tuesday, said one of the sources, who declined to be identified as the discussions are not public.

The so-called stalking horse bid by the private equity firms would serve as the baseline offer for the business, which also includes Dolly Madison bread and Hostess cupcakes. It could still be topped by others at an auction.

Dean Metropoulos, No. 360 on the Forbes 400 list of America's wealthiest people, is a packaged foods veteran who was once the joint owner of brands such as Duncan Hines baking mixes, Vlasic pickles and Swanson frozen dinners. In 2010, his firm bought Pabst Blue Ribbon beer, the no-frills brew popular with young East Coast hipsters.

His son Daren, a principal at the firm, confirmed earlier this month that they were working on a bid. Neither Daren, nor a spokesman for Apollo were immediately available to comment on Tuesday. Hostess declined to comment.

Apollo, founded by banker Leon Black, has invested in consumer companies before, including in CKE Restaurants and Claire's Stores Inc.

Hostess was granted permission by a U.S. bankruptcy court judge in November to wind down its business and liquidate its assets after a strike by a baker's union crippled the 82-year-old company's operations.

The sale of assets, which range from Twinkies and Wonder bread to real estate and baking equipment, is being run by Perella Weinberg Partners. The lead banker on the sale, Joshua Scherer, has said there was great interest from many parties in the assets.

Earlier this month, Hostess chose a $390 million offer by Flowers Foods, maker of Tastykake products, as the stalking horse bid for several brands including Wonder bread.

On Monday, Hostess said it chose McKee Foods Corp, maker of Little Debbie snack cakes, as the initial bidder for its Drake's cakes, which include Ring Dings, Yodels and Devil Dogs. It also chose United States Bakery as the lead bidder for four of its smaller bread brands plus bakeries, equipment and depots.

Hostess also filed a motion on Monday to stop paying retiree benefits to its former employees, saying that its lenders only agreed to fund the benefits through February 2013 due to a delay in the appointment of a retiree committee.

(Reporting By Martinne Geller in New York; Editing by Gerald E. McCormick, Bernard Orr)

By Martinne Geller

Stocks treated in this article : Apollo Global Management LLC, Flowers Foods, Inc.