There hasn't been too much discussion about this, but the first point is to narrow down exactly what functionality would be desired on mobile.
A while back someone (I think it was @meeDamian ?) added push notification functionality for coinjoins from makers; that would be basically trivial.
Then you could go further and have like a control panel for remote access on phone, and still have same basic joinmarket on home machine. To go even further (1/2)
... and embed the wallet into the phone would be a substantial step up in work, and to not require an external jmdaemon, ie 100% on phone, even more (whole can of worms including Tor).
(jmdaemon was something i added in the rewrite in 2016/17; you can have the communications with peers entirely separated from the wallet, and the two talk to each over over TLS. At least one user actually does this)
(instance image by мøтħer ¢røω)