I checked the play on my wheels and found side to side play and not up and down play.

My mechanic told me that it's the wheel bearings but I don't think so, there would be up and down play too.

Upon further inspection of the front end, I noticed that the driver side tie rod adjustment sleeve was loose, I could rotate it by hand with the wheels on the ground.

I just want to know if this would cause play in the wheels.

 

To determine wheel bearing play, with the car up on jack stands grip the tire at the 11:00 and 5:00 positions and rock it in and out. The tie rod ends will rotate on the pivots.

 

The sleeve being loose on it's own would not create 'play', but could contribute to alignment problems. Worn tie rod ends could allow 'play'. But you are likely correct, a bad or loose wheel bearing would have play side to side and up/down.

 

Agreed. The side to side play could be tie rod ends or other steering components.