NEW YORK — The indestructible Twinkie appears to be one step closer to a comeback.

Hostess Brands is close to announcing that it has picked two investment firms — C. Dean Metropoulos & Co. and Apollo Global Management — as the lead bidders for its Twinkies and other snack cakes, according to a source close to the situation who was not authorized to comment publicly on the talks.  

The joint “stalking horse” bid would set the floor for an auction process that lets competitors make better offers. A judge would have to approve any final sale.

After years of management turmoil and turnover, Hostess declared it was going out of business and selling its brands in November. The company, based in Irving, Texas, has already announced separate lead bidders for its other brands. McKee Foods, which makes Little Debbie snack cakes, was picked as the lead bidder for Drake’s cakes, which include Devil Dogs, Funny Bones and Yodels.

Flowers Foods, which makes Tastykakes and a variety of breads, was picked as the lead bidder for six of Hostess’ major bread brands, including Wonder.

United States Bakery Inc. was picked as the lead bidder for a number of smaller bread brands.

Citing sources close to the situation it did not name, the Wall Street Journal reported Tuesday that the offer for Twinkies and other snack cakes by C. Dean Metropoulos and Apollo would be for more than $400 million. The report said that the deal could be disclosed as early as Tuesday. C. Dean Metropoulos owns Pabst Brewing Co.

A representative for Apollo declined to comment. A representative for C. Dean Metropoulos did not return calls for comment.

Hostess has stressed in bankruptcy proceedings that it needs to move quickly in the sale of its brands to capitalize on the outpouring of nostalgia and media coverage prompted by its demise. The longer the cakes and breads are off shelves, the more people will become accustomed to eating cakes and breads by rivals, the company has said.