1 Store live mussels in the refrigerator in an open container and cover with damp cloths or paper towels. 2  Mussels must be kept alive before cooking.3  To freeze, place whole mussels in heavy-duty freezer bags.4  Freezer time shown is for best quality only — foods kept constantly frozen at 0° F will keep safe indefinitely. Mussels must be kept alive before cooking. 2  To freeze, place whole mussels in heavy-duty freezer bags. 3  Freezer time shown is for best quality only — foods kept constantly frozen at 0° F will keep safe indefinitely.