"I do know that he is close to many other undergraduates in the social circle, and many of them do take his class." (The bolding is my own.)
The key word here is "close." I don't know exactly what you mean by this, so I will include some specific examples in my answer.
How should he behave in this situation? Is it ok for him to be part of a social circle with many undergrads, knowing that some of them may take his class in the future?
Your university should have a policy posted online about this. But the basic advice, I believe, is generally:
The professor should inform the department chair if there are any students on his class roster that are related to him or have a close friendship with him. In other words, if Roger Smith is on his class roster, and he sometimes goes for a hike on Sunday afternoons with Roger, in a small group, and then has him over for dinner -- the department chair needs to be told.
On the other hand, if he sometimes gives Ellen Jones a ride home after church because he lives in the same direction as Ellen, that's probably not worth telling the department chair about. However, in case of doubt, it's best to inform the chair and let him/her decide if anything needs to be done.
If a close friendship starts to develop during the course of the semester, the professor should either back off and put the developing friendship on hold until after the semester is over, or proceed as above. Reason: it's not enough to behave ethically. It's also important to avoid the appearance of impropriety.
Yes, it's okay for him to be part of a social circle with undergrads, knowing that some of them may take his class in the future. However, if the department chair is getting these notifications, semester after semester (i.e. there are a lot of Roger Smiths), the chair might sit him down and ask him to try to expand his social circle to include more people his own age.