I'm a little confused -- is your pregnancy physically obvious? If so, I just wouldn't worry about it at all as they'll know when they see you.
Regardless of whether it's obvious and regardless of what your current supervisor has to say about you, I personally would want to be the one to break the news to my current supervisor that I was considering or had been offered a transfer. (Ideally I would want the offer first, or a strong indication it was coming.) I would think the hiring manager would understand that, and would respond to some normal questions about next steps in the process. You can even say, "When you're ready to talk to my supervisor, please just let me know so I can break the news to him in person: we have a great working relationship and I think he'll be sorry to see me go." Or whatever phrasing sounds natural from you and not like you're trying to manage what your supervisor says.
I have no idea whether it's legal for your supervisor to share health news when contacted, but we all know it happens.
Good luck!