Is this on a concrete wall? Concrete walls are never completely cured and free of water, so they always have some moisture in them. Moderate levels of moisture in a concrete wall will not damage it.

What many folks usually do is seal the wall on the inside with a coat of moisture barrier paint, and then insure the grading and downspouts keep water away from the exterior side of the concrete wall. However, if you want to finish the basement walls, you can try adding thick plastic sheeting up against the concrete as an additional moisture barrier, or a more effective solution is closed cell foam at least an inch thick.

Since both the closed cell foam and the concrete wall are inorganic, there shouldn't be anything to feed mold and cause it to form next to the wall. However, mold will form on untreated wood and drywall when they get wet, so they have to be installed so that they do not have contact with any moisture in the wall or floor.

Bruce