The easiest way to put this is that there appear to be symbiotic relationships where beings consume aether from other beings, particularly primals, and that's the closest that FFXIV gets to a "vampire." Â However, this aether is also easily drawn from crystals.
Final Fantasy as a whole has some other games with canon vampires (the Marquis Elmdor in Tactics being the first to spring to mind), so if they were going to have blood-sucking vampires in the game, they'd be there. Â It's possible they exist and haven't been introduced, but they are presently not part of the canon. Â You'd be on your own and working on a person-to-person basis.
Final Fantasy as a whole has some other games with canon vampires (the Marquis Elmdor in Tactics being the first to spring to mind), so if they were going to have blood-sucking vampires in the game, they'd be there. Â It's possible they exist and haven't been introduced, but they are presently not part of the canon. Â You'd be on your own and working on a person-to-person basis.