Can I lay tile on top of existing stick-on vinyl squares?

It would be best to lay it straight on a prepared surface.like concrete or wood.Vinyl tile is a quick fix but can loosen if gets wet especially in an environment where it would be susceptible like a washer leakage.

You could lay a cloth over the tiles and iron them to soften up adhesive. They will lift right off.

Remove the vinyl tile. New tiles need a level and solid substrate. Any damage to the old tile will transfer to the new tile.

The problem will be the tiles will move and any grouting will continuously crack out. Sorry ... but vinyl tiles will need to be removed and would suggest installing cement board before tiling. Substrate HAS to be solid.

He's right . Laying tile is hard ,time consuming work and it will all be for nothing if the vinyl comes loose for any reason . You would do well to scrape it up.

Samantha Lodge - The best application would be to remove the self stick because they have a tendency to come loose. Prep the floor if concrete wash and dust free, wood sweep and dust removal before laying a new floor. If you are using ceramic or porcelain tile I suggest you try a product cal, " Ditra" which will help with floor movement and moisture which can cause tile to crack. You can find this product at Home Depot, Lowe's or Flooring stores. Watch You Tube videos for help on installing tile.

I would not recommend laying tile over stick-on tiles. If the stick on tiles ever loosen from the floor, it will ruin your ceramic tile. Either remove the stick-on tiles, or lay a sheet of wood or cement board over them before laying your new tiles.