There could be a number of reasons. He feet could hurt or there is some sort of irritant that he's trying to nurse. He could be itchy in that paw and can be cause by something he stepped in or his diet, allergies. He could be developing an obsession of the oral fixation sort and that could stem from boredom, anxiety, nervousness, etc. May he keeps stepping in food crumbs and is just trying to chew it off night after night, lol. I would take him to the vet to get him checked out.
He might be doing it out of boredom or he's got allergies. My dog chews on his tail out of boredom, so when he does, I give him a toy and he will forget about his tail. If he's allergic to something, you'll have to find out what it is. It could be food, pollen, etc.
Also ... just to add ... if he chews on them for too long and they become raw he could cause a bacterial infection in his skin. I would honestly take him for a vet visit and see if it is allergy related or neurological.
Arthritis will cause that, too, as will the nails being too long. Dogs have an instinct to lick wounds because their saliva contains an enzyme that kills bacteria. So, for a dog, licking a wound could be life saving. They extend that to licking anything that hurts, though, so they end up licking and chewing themselves raw trying to relieve joint pain.
If it is arthritis, there are treatments that can help with pain. Definitely go to the vet.