This is a difficult question to answer, as we don't really know who Satan is or what his relationship status is. However, we can speculate based on what we do know about him. Satan is generally portrayed as being a male figure, and he's often shown as being alone. This could suggest that he doesn't have a wife, or at least not one that we know of. Given his nature as a fallen angel, it's also possible that he isn't capable of love in the traditional sense.