Cat Sleeping With Face Down . But if it's visibly pressing its head against a wall when awake and is obviously not relaxed, it might be time to visit a vet. Comparatively, while it is possible cats will sleep while head pressing, you'll notice this behavior more frequently while your cat is awake. Found my cat sleeping face down. This is the look he gave from www.reddit.com Cat sleeping positions face down. Comparatively, while it is possible cats will sleep while head pressing, you'll notice this behavior more frequently while your cat is awake. One of the most interesting of the cat sleeping positions in the monorail, or when your cat lies on the arms or backs of chairs, sofas, staircase banisters, fence posts (and so on) and dangles down some or all of his legs.