Great Danes are big dogs, if you are feeding dry meal then it will drink, if you really think it is drinking excessivly then you should assure yourself that there is nothing wrong with him, for example, liver problems, diabetes, and have a blood test conducted at the local vets.
My dane is fed mainly dry food and he drinks A LOT. He also loses a bunch of what he drinks on the floor. I don't think they will drink more than they need.
It might just be me and not trying to sound rude, if you started drinking a lot of water should we tell you when enough is enough. Dogs will drink water when they are thirsty that is all there is to it. Like the other said they lose a lot of it to the floor when they move away or in mine dane's case as he drinks it comes out the sides of his mouth, and then when he moves away floods the floor.