How long has this been going on for? Is it all the feet or just one?
It could be a local irritation as terambulan says, caused by a chemical or sensitivity to something.
It could also be an allergy, as itchy feet can drive dogs nuts as they lick and chew at them all the time. It doesn't necessarily have to be to something thedog has walked on, it could be a manifestation of a reaction to anything the dog is sensitive to.
A skin fold infection, between the toes, could also cause severe itching.
Think pup needs a trip to the vet to get his feet checked out, possibly a course of antibiotics or antifungals and a buster collar to stop the licking!