The best I could find was the following from "Unseen Attackers and Targets", PHB pg. 194:
When you attack a target that you can’t see, you have disadvantage on the attack roll. This is true whether you’re guessing the target’s location or you’re targeting a creature you can hear but not see. If the target isn’t in the location you targeted, you automatically miss, but the DM typically just says that the attack missed, not whether you guessed the target’s location correctly. When a creature can’t see you, you have advantage on attack rolls against it.
If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses.
This implies that a non-hidden creature can still be tracked, but since it talks about guessing the location, I'm not sure if this means you can perfectly track the location or whether you can just guess (i.e. the DM says "the invisible enemy goes towards the door" so you know roughly where they are relative to your surroundings but not to the square, as you put it).
So, my conclusion is that you do not know where they are to the square, but they'd need to Hide for you to not know where they are at all.
