It may just sound like a pipe-dream, but it could be a reality!
The Director for Breath of the Wild has been confirmed to be Hidemaro Fujibayashi, the same man who not only directed Skyward Sword but also the Minish Cap - the game that went into depth on Vaati’s backstory and character.
There isn’t a ton of evidence for it yet besides the connection with the director, but there is no reason it cannot happen!
1) Ganondorf usually inst the ONLY villain when he appears (Except for a few), he is often accompanied by other villains.
2) Vaati is the only other recurring Zelda villain other than Ganondorf/Ganon that has appeared across timelines (If you bar Skullkid who really isnt a villain)
3) Vaati hasn’t appeared in a Zelda game since 2004 (Minish Cap)
4) Vaati has appeared in the Pre-Split Timeline as well as the Child Timeline. This means that he exists in the Fallen and Adult Timlines, but has yet to appear.
5) Breath and Wind go hand and hand! :)
In conclusion: It’s about time for the Great Wind Mage to be resurrected once again and Breath of the Wild’s massive scope may just be the opportunity!