Out of all the jobs that have been seen in the FF series they could still use:
- Oracle
- Devout
- Sage
- Geomancer
- Songstress (Only because FF14 lacks a dedicated support role. Though you could make a case for it being another Ranged DPS like Dancer.)
- Chemist/Salve Maker
- And if they REALLY want to be trolls they could pull from Bravely Default's Merchant class because it does have healing mechanics. (IT HAS A SKILL CALLED BIG PHARMA)
There's a few others that can also heal (I'd die of laughter if they gave us Mime as a healer) and a few of these overlap with existing classes. Due to the overlap Chemist and Geomancer are the most likely, though Geomancer currently has a lore overlap with Astrologian in 14.