In the past, I would always pull up such tiles and start from scratch. I hate thinking how much asbestos I breathed in over the years renovating.

They can still be pulled up safely following procedures detailed in the Inspectapedia link below and in sub-links to the University of Minnesota etc.

But if the tiles are intact, I would use one of the isolating/insulating underlayments--extruded polystyrene, Delta FL, Dricore (or any of their equivalent competitors) and your floor covering of choice.

The problem with just covering the tile with another finished floor are several. If any of the underlying tiles are loose, it will hard to secure the new floor; tiles may telegraph through the new surface; vapour impervious coverings will accumulate water that will feed mould; and you haven't created a way to handle water vapour drive upward through the concrete floor.

Spend the extra money and do it right.

Here is a link that might be useful: Floor Tiles That May Contain Asbestos

Worthy,

I appreciate so much your response to my question. This link is going to be very helpful. Thank you so much.