It's normal for cats to drool while sleeping when they're tired, but they only drool when they're in a deep sleep, and even then, it's usually not excessive. Most cats drooling while sleeping is normal and nothing to worry about. 
While drooling is mostly normal during sleep, it can sometimes be caused by ingesting something harmful, oral diseases, or other health issues, and it's not limited to sleeping. If you notice your cat drooling abnormally, remember to take it to the vet for a checkup as soon as possible.
Cats may drool due to gastrointestinal problems or liver disease, especially when they are sleeping and relaxing. It is best to treat them as soon as possible.
