Magnetism exists whenever electrically charged particles are in motion, as in the movement of electrons in an electric current; Magnetism also arises from alignment of magnetic dipoles arising from quantum-mechanical spin...as in bar magnets.
As far as I know those are the only sources...If magnetic monpoles are ever found, that might do it, but none have been found so far...
Depending on exactly what you mean, a rotating black hole might fit...but it seems that even though one does not contain any "matter" as we know it, that's still the origin of the magnetism...so it's a bit of a stretch...
I'd agree it seems impossible today, but who knows about tomorrow?? It's perhaps similar to asking about antigravity...we don't know how do do that either... yet...