No, mice won’t bite you in your sleep unless you have food crumbs on you or you smell like food, or if you are a very deep sleeper and don't sense the mouse coming up to you. In most cases mice do not bite sleeping people, but rats have been known to charge or leap at a person, and when handled, wild rats and mice are capable of squealing and biting, which is why if you have an infestation of mice in your house, you need to be careful about your sleeping quarters.