Rumors have been circulating about Nintendo's NX returning to a cartridge based platform for a little while now. Those rumors are about to get a bit more questionable (or validated, depending on what you think of them) as a recent trademark seems to suggest the next Zelda may be on cartridges.
Uploaded to Neogaf by user SmellyCat, according to the US trademark system The Legend of Zelda: Breath of the Wild includes "videogame cartridges" under it's Goods and Services description. The same description can be found for 3DS games including The Legend of Zelda: Triforce Heroes, as well as the recently announced Ever Oasis and Pokemon: Sun/Moon.
Interestingly, if you look at the listing for the Wii U titles The Wonderful 101 and even the recently released Tokyo Mirage Sessions #FE, you'll see that no such description exists, only including "videogame discs." Since Breath of the Wild will also release on Wii U it also includes this description.
While this is hardly hard evidence that the NX will return to cartridges, these details coupled with the NX's initial patent not featuring a disc-drive, would seem to suggest that there may be a kernel of truth in all of this. We won't know for sure until closer to the NX's launch.