Judge Robert Drain of the U.S. Bankruptcy Court in White Plains, N.Y., had urged Hostess and The Bakery, Confectionery, Tobacco Workers and Grain Millers International Union to try to resolve their differences, reminding them that 18,000 jobs were on the line.
But mediation was unsuccessful, according to a Hostess statement released late Tuesday. A lawyer for the bakers union said he had no comment.
An attorney for Hostess told Drain on Wednesday that closing down the company would take a few months.
Hostess shut down its plants last week, claiming a strike that was started on Nov. 9 by the union crippled its ability to maintain production.
The union blames years of mismanagement for the impasse.
Even if Hostess goes out of business, its popular brands will likely be snapped up by buyers and live on. While Hostess' sales have been declining in recently, the company still does about $2.5 billion in business each year. Twinkies alone brought in $68 million so far this year.
ABC News and The Associated Press contributed to this report.