Dogs drool for a lot of reasons. It's usually because they feel nauseaus and they need to vomit, they have a mouth or tooth issue, or they are really excited.
When you see it during sleep, it's very often caused by the mouth or tooth problems mentioned above or it could be a product of his dream states. Much like people, dogs will dream of exciting things, even food in some cases because this is something that drives them. When this happens, their bodies respond as though they were awake.
I would definitely go ahead and see the vet with her for an oral exam to rule out a mouth or tooth problem and to discuss your concerns with your vet.
Then go from there.
Let me know if you still have questions or if you want to discuss this more.