With my stepson, he did have this problem. We monitored what he was drinking after about 3p, and had him go to the bathroom, every 2 hours after that. After 3p, he got a drink with dinner, and it was only 1 cup, and if we felt he didn't get enough liquids early, he would get a second cup of water, but otherwise, we would only give him a half cup of water. This sounds like a long time to go without liquids, but it's not. When you think about it, you get a cup of liquid with dinner around 5-6, and then about 2 hours later is bedtime. so it's perfect. This really helped a TON for us.
We had to remind him to go to the bathroom. Otherwis, he wouldn't pay attention to his body, and then would make a mad dash to get there before he went in his pants. So by making him go every 2 hours, he forced him to start listening to his body. And now no problems.
Even though he isnt potty trained yet, if he stop te drinks and put him on the potty every two hours, it will help him train, but it will help out as well.