Waking a sleeping Cohen when there is a dead body in his room

Is there an obligation to wake a sleeping Cohen when a person has passed away in his room, or since he is sleeping and considered as if he were legally incapable, and there is no need to wake him?

There is a commandment for anyone who knows that he is a Cohen to wake him in a case of biblical impurity, such as being in the same tent as a deceased person. However, in a case of rabbinic impurity, such as when the windows and doors are closed and the impurity has no way of leaving the room, there is no need to wake him.

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