It can also be an embouchure problem, example if you were to have too much bottom lip over your bottom teeth when playing, then what can happen is a pool of spit can build up around your bottom lip, and when you blow into the mouthpiece – you can be blow more spit onto the reed.
Sometimes if you have been eating a sweet or you have bits of food trapped in your mouth, this can also cause your mouth to produce excess saliva which you want to avoid when blowing wind instruments. A good idea is to brush your teeth and rinse out your mouth before playing.