Amelphia Tarramon, the first quest giver at the Mages Guild in Old Ebonheart, has the duties topic before you become a member of the Mages Guild. She says:
"I think I might have something you can do. I've been experimenting with some alchemical ingredients that you can only find on the mainland of Morrowind, and I've run out of three of them. You could help replenish my stores."
This doesn't actually let you start the quest, but it's definitely a line that shouldn't be said without membership.