Our cat Whiskers comes to wake me up almost every morning by walking on me. Once I am awake he will flop over on my chest while he gets his head rubbed and is petted. Once he has had enough, he expects me to get up to let him outside. It's an established routine for us.
Sounds like our morning routine
Mine never did. In winter she used to sneak under the doona & curl up around my feet or lie against my back.