It was asked ages ago for something like DRG's wyvern to return (and repeatedly too), and Yoshi basically said "no". We do have several dragonling minions which look a lot like FFXI's DRG wyvern, so that's the closest you'll get I'm sorry to say.

Also it's clear SE have pretty much moved away from adding further (non Chocobo) companions to the Chocobo Companion system, instead we've got the Grand Company Squadrons (which can be used in certain dungeons), and the soon-to-be-added Trust NPC system that will be able to be used to take the player through the main scenario (based loosely on FFXI's ironically enough).