Hi, I agree that milk is not a great option for a cat. I'm wondering if it could have something to do with the water itself. You could pick up some bottled water at a convenience store and put that in a dish and see if your cat goes for it.
As someone else mentioned, the dish used can really make a difference. Cats generally don't like their whiskers to touch the edges when they are eating or drinking. Plastic dishes may effect the taste of the water so you might want to switch to ceramic if you haven't already.
The suggestion catlady posted about adding water to wet food is something I do, just to make the wet food stretch since I have a few cats and it can get pretty expensive. They really seem to prefer the 'soupier' supper, especially if it is the cat tuna.