The Wii U is only backwards compatible with Wii software and not GameCube software. Therefore, there appears to be no reason for the Wii U to support a GameCube controller. Appearances can be deceiving, though!
Many Wii users prefer to use the GameCube controller for certain Wii games. Super Smash Bros. Brawl and Mario Kart Wii are a couple of great examples. Not as many Nintendo fans jumped on the Wii wheel and nunchuk bandwagons as the company had hoped. Now there is a solution for those Nintendo fans who want to play one of those games on the Wii U without having to use Wii controls.
A third party adapter has been made available on Amazon that will allow players to use a GameCube controller with their Wii U. It even allows for turbo functionality, which seems to be a requirement on third party devices since 1994.
Wii U owners who are looking for a way to play their old Wii games with a GameCube controller should check it out. Remember, it’s just an adapter. You still need your own GameCube controller for it to work.