How can I ask my friend if he’s autistic?

I’m a ND (ADHD) woman. I went out with a guy I met on Hinge and REALLY liked him. He has chronic illness that he’s trying to get under control, and so he had to end the dating relationship. He and I are “friends” now in that I really care about him, we talk and catch up occasionally, and stay in touch. I still like him and want to be more than friends. He doesn’t think we can date until he’s “cured.”

I highly suspect that he is autistic (I can share why if curious — this all-or-nothing thinking about dating is part of it) and I highly suspect that autistic burnout and lack of self-understanding is contributing to his chronic fatigue and burnout. I just want to help him. I’m not sure if he has ever been diagnosed, which is why I want to ask him and/or gently suggest.

How can I do that in a way that is okay? Or should I just not because it’s not my place? I am really afraid of overstepping his boundaries. I want to build his trust and I don’t want to push him away. Would really appreciate advice!