Well, you can do that in two different ways.
If the player is overlapping the object you can compare player coordinates with the object coordinates and with this determine if the player is by the side of the object or above it or whatever.
However doing this requires a lot of testing and your game my get little buggy depending on the size of the sprites and speed they're moving.
The other way is to create invisible and objects and attach them to the visible object. Note that these invisible objects should be smaller than the first one, and they should be at least 1 or 2 pixels beyond the are of the visible one.
So you will check the player collisions to the invisible objects instead of the visible one. If the player collides with the invisible object attached to the left side of the visible one... then the player is colliding on the left.
This will make your codding easier and the game will run smoothly and with less bugs, whoever creating too many objects on a single layout will slow down your game performance