The basement floor is often cooler than the basement air temperature, and adding carpet drops the temperature even further.
The floor temperature under a carpet may fall below the dew point of the air if the basement humidity is high enough. In this case, a little moisture will pool beneath the carpet, creating ideal circumstances for mold production. Moisture formation may be so subtle that it is not visible from the top of the carpet.
Carpeting or area rugs may work if the basement floor is already insulated or has under-floor heating. However, if you have a basement moisture problem, you must address it before putting any floor covering, particularly carpets.
Excess moisture may be readily tested by attaching a piece of plastic sheeting to the concrete floor and sealing the edges with duct tape. Allow the plastic to sit for 24 hours. If condensation forms behind the plastic, you and your contractor must conduct a mitigation strategy.