Is there a problem with stainless sinks on tile countertops.?

I can't imagine why not. Only problem I can see is if the tile is marble, do not use Plumbers Putty as a seal around the edges. It will stain the marble. I have installed many stainless sinks on tiled countertops.

The only problem I can see is fitting the new sink into the existing hole. You might have a problem if that is not an exact match and you need to cut a new hole or need a smaller hole.

You say you have tile on a concrete base. Do you mean concrete backer board? If so, that should not be a big problem but if you mean solid concrete then that could make fitting a new sink difficult.

Our previous house had a tile counter top and a stainless steel sink. It worked just fine.

Based on your follow up information, I can see why it would be a problem. You will need to find a sink with a cutout requirement that matches your existing cutout, otherwise making a new cutout can be difficult.

I had a tile countertop in my last house. With a stainless sink, and it worked just fine. It had a ring of caulking around it, under the edge, so it was easy to clean. Talk to the people at a major building supply company.

I'm not a builder but I can see no reason why two can't be used together.