The closing of the facility could result in more than 200 lost jobs, according to a story on the al.com news website.
Officials from Keene, N.H.-based C&S did not return calls for comment.
The C&S Birmingham facility, which does business as Birmingham Logistics, could close as early as Aug. 28, according to the al.com story.
Decatur, Ala.-based Belle Foods filed for Chapter 11 bankruptcy protection in U.S. Bankruptcy Court in Alabama on July 1.
Belle Foods, a privately held company, operates 57 stores in Florida, Georgia, Alabama and Mississippi under the banners of Belle Foods, Piggly Wiggly and Food World.
In a July 5 filing, the company asked the court for permission to try to sell 13 of its 57 stores. The court granted that request and, based on the level of interest in those stores, in a July 24 filing Belle Foods said it wanted to try to sell the other 44 stores.
In the original bankruptcy filing, Belle Foods said it was obligated to pay C&S about $900,000 on a pension withdrawal liability note and $5.1 million in accounts payable.