the appearance of the greater soul gem in morrowind (a cluster of crystals) would seem to suggest a mineral origin, as does the "geode veins" in Skyrim, but I don't think more than that is ever revealed. I'm racking my brain for anything related, but its been quite a while since I last brushed up on lore, and the only things that come to mind related to soul gems are
1) the passage in a book (the maddness of pelgius I think?) where a soul gem is described as having a sort of spectral wolf visible inside it,
2) another possible origin of soul gems being meteoric glass like welkend and varla stones (magic from the sky I think)
3) a passage in a book (Souls black and white I think) adivising caution when handling soul gems to prevent them from absourbing part of the handler's soul
that's all I can think of, but I'll do some digging, interesting subject, this