Given that 1.5 litres per day is the recommended minimum for an adult I would say yes, that's excessive. My DS liked his water too at that age but I'd say he would have drunk about 500mls a day (milk on top of that).

DD is 18 months and drinks about 600mls of milk a day (she won't eat dairy so I let her have more than DS did) plus some drinks of water but once again, that would not be more than 400mls (more on a hot day).

My first thought was diabetes too - not that I know anything about it, just anecdotally I have heard that a raging thirst can often mean undiagnosed diabetes. Please note that I am hardly an expert, this is just a titbit of general knowledge that I've picked up from somewhere! I'd be asking your child health nurse for an opinion.