A steak can keep in the fridge for 3 to 5 days. You might notice that the meat turns grey after a day or two. This process is perfectly normal. A grey steak is still safe to eat. Myoglobin molecules in the steak contain iron. This iron is oxidized when it comes in contact with oxygen. The oxidation results in a grey color. To prevent or slow greying of meat, ensure it is tightly wrapped in plastic wrap to discourage contact with air.