Probably not. That looks like it's soft and fluffy, so it's probably just mycelium. It's no big deal. More fresh air might get rid of it, but it's probably causes by high humidity. My mushrooms have pretty much always grown mycelium like that on the base. It's actually kind of cool. Sometimes it can even get rhizomorphic growth, and look all fractaly.
It's really rare for mold to grow on a live fruit body, or on heavily colonized substrate. Spores are sure to land on it, but they won't germinate because the mushroom has its own defenses, and there wouldn't be enough available nutrients to germinate mold.