A deal, part of Hostess's bankruptcy reorganization, is not yet final, said the source, who declined to be identified as the discussions are not public.
The so-called stalking horse bid would be for more than $400 million, according to the Wall Street Journal. It would serve as the baseline offer for the business and could be topped by others at an auction.
Spokesmen for Metropoulos and Apollo were not immediately available to comment. Hostess declined to comment.
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.
(Reporting By Martinne Geller in New York; Editing by Gerald E. McCormick)