My 14 year old poodle was doing the same thing a couple years ago so I took him to the vet. He had a few teeth that were bad, meaning loose and infected. Once the teeth were removed, he was back in tip top shape. Does your dog have bad breath? That's another sign of dental problems...good luck.
This is not a typical sign of diabetes. Diabetic dogs drink more, urinate more, have weight loss, and may become anorexic or lethargic. Licking the mouth could be sign of nausea--this can be caused by a variety of problems. It would be best if you had your dog examined by a veterinarian. Initial bloodwork will rule out diabetes and many other conditions.