Several observations are revealing the widespread occurrence of mildly relativistic wide-angle AGN winds strongly interacting with the gas of their host galaxy. Such winds are potential cosmic-ray accelerators, as supported by gamma-ray observations of the nearby Seyfert galaxy NGC 1068 with the Fermi gamma-ray space telescope. The non-thermal emission produced by relativistic particles accelerated by the AGN driven wind observed in the circum-nuclear molecular disk of such galaxy is invoked to produce the gamma-ray spectrum. The AGN wind model predicts a hard spectrum that extends into the VHE band which differs significantly from those corresponding to other models discussed in the literature, like starburst or AGN jet. With dedicated simulations in the context of the Cherenkov Telescope Array (CTA), we demonstrate that, considering 50 hours of observations, CTA can be effectively used to constrain the different acceleration models.