Head to Sinking Sands to speak to Captain Shoreflow ( -2161, -228, 16 ) /waypoint -2161, -228, 16. Turns out it's not his bird.
Then go to Mystic Lake off of the Isle of Mara and talk to Captain Mord ( 42, -36, 277 ) /waypoint 42, -36, 277. He doesn't want the bird either.
Next visit Greater Faydark and talk to Captain Z'Sxhitar ( -536, -27, -641 ) /waypoint -536, -27, -641 at the Shores of Growth near the Nursery. It's not his bird either.
Finally go to the Enchanted Lands docks and talk to Captain Screewoggins ( 39, 4, 116 ) /waypoint 39, 4, 116. Turns out he's the rightful owner of the parrot, and will complete the quest. But you do get to keep your new pet.