Has he mentioned something like that directly?
Yes he has.
Interviewed by the Chicago Tribune Editorial Board a few days ago for over an hour. Trump speaks about it so see around the 55 minute mark in the Tribune video.
Trump speaks about a private healthcare system; removing state line for healthcare and gives an example for a better deal in another state; taking care of people who are without insurance by making deals with hospitals and says this will mostly be private and not government; and it won't be as good as people paying for insurance, but he believes it will be pretty good. Don't take my word for it - listen around the 55 minute mark in the video. Plenty there to counter the naysayers who selectively listen. Listen to the whole interview it's good.