Everyone's different so don't generalize this to all Aspies, but for him, maybe you talk about what it's like to be depressed very briefly if he's said he is, and you could ask if he's having a hard time or something.
"How do you feel?" is really old ended and can be anxiety provoking. Sounds like you would be the social glue in the relationship.
If you and he get close, what would will be like for you? Can he meet your needs for closeness and connection, or will you never be able to really depend on him when you need to because he doesn't deal with depression, can't talk about it in himself, and perhaps not in others, either. I think it's worth thinking about where you want to go together.