First check the steering column; particularly find where the u-joint is (it is under the dash) and inspect it. it can either wear-out or the bolts that tighten it to the steering shaft could have loosened. If you only feel the free-play when the engine is on, then the likely problem is the connection from the electric power steering motor (I assume your car has electric PS) to the steering column. On most cars their is a plastic or rubber gear that transmits torque from the electric motor to the steering column or steering rack. This “gear” can wear out. With the engine off, try to observe or feel if there is any overall free-play in the system. You can do this by placing one hand on the front tire while wiggling the steering wheel (you might need an assistant). If there is no overall free-play and you still have the feel of free-play when the car is on, it is probably the PS motor gear. Finally, it is possible that your steering rack is worn out, but this will show in the overall free-play when the car is off.