I am currently in the process of remodeling my basement level for the second time and have pulled up the carpet from a 14x17 area that was damaged due to pets. Under it, I found 9x9 tiles and under those black something over the concrete. I've been told that the tiles and black "stuff" contain asbestos. If I can't safely remove those pieces, what can I lay over to create a level floor other than carpet? Many of the 9x9 tiles are warped from water damage many years ago (hence the first remodel). This second remodel is to make small improvements to get the house for sale. I was looking at laminant flooring.

My question is can I lay something over the asbestos containing flooring and not have worries for a home inspection at the time of selling the home that would cause a decrease in value or cancel the sale or do I have to remove the asbestos containing flooring?

First, no one can say a tile or adhesive has asbestis just by looking at it, it must be tested to know for sure. Get a test kit or call a pro. Asbestis can be contained by sealing in a new envelope (encapsulated) of new tile or flooring. Below grade flooring must be carefully selected because not all laminates work well in the presence of moisture.

First I'd recommend you test the tiles and what is underneath for asbestos and safety. Have a pro give you a report.
If the floor is asbestos free or it is safe to keep it there you might want to try floating floor solutions specifically developed for below grade spaces such as ThermalDry or MillCreek. They are 100% waterproof and inorganic interlocking tiles or laminates.
And since you do no not need adhesives to install it, you can easily remove if you ever need to check the state of the floor underneath.