Your best bet would be to look on the Hyundai forums for the solutions they've used. I don't see it as unrealistic that this should be doable, provided your stock HU has a compatible auxiliary connection in the back. For that you would use something like a Parrot module, but it wouldn't be as integrated as a stock solution would be.
My honest recommendation would be to look into upgrading your stock head unit to an aftermarket one that features built-in Bluetooth. You may lose some of the functionality of your original deck, but the gains in sound quality and compatibility with third-party devices outweighs what you'll lose in my opinion. There's options as inexpensive as the Clarion CZ702 (which has the Bluetooth mic built into the faceplate) up to other solutions that feature a wired microphone that you can route anywhere within the cabin.