Working with a Ph.D. supervisor that may have to take medical leave?
I'm a big fan of saying "donkey" when it's a donkey, rather than beating around the bush and calling it a grey-colored, short-legged horse.

The thing is: Everyone, including the professor, understands that any leave of absence he's going to take will affect you in a number of important ways. It's not like anyone can be mad at you for wanting to bring this up. So that's what I would do, acknowledging the awkwardness of the situation, in a personal conversation:


  Professor, I would really like to work with you, but I have one last, awkward topic I'd like to ask you. When talking to others in the department over the past couple of weeks, someone mentioned that you may take an extended leave of absence for personal reasons. It's really none of my business to ask you about this, or the reasons for this, but if I signed up with you, it would be something that clearly affects me as a graduate student. So I wanted to bring it up and see whether that was true or not.


That gives the professor an opportunity to tell you how it is. He will understand why you ask, and tell you about as much as he chooses to share. If there really are medical reasons, you're not likely going to get any better answer by going around his back and asking others in the department.

I'll also mention that over your career as a grad student, you're likely going to have a number of awkward conversations with your adviser anyway. You may have to talk about money issues (grant runs out and it's not clear if the follow-up grant will be approved), breaking up with your girlfriend and falling into a hole for a number of months, being sick for an extended time, etc. Professors have awkward conversations with students all the time, and the better ones have figured out how to have them without it being that big a deal. So talking about something you have a legitimate concern about should be par for the course.