  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 extend in the very high energy
band which differs significantly from those corresponding to other models
discussed in the literature, like starburst or AGN jet. We present dedicated
simulations of observations through the Cherenkov Telescope Array (CTA), the
next-generation ground based gamma-ray observatory, of the very high energy
spectrum of the Seyfert galaxy NGC 1068 assuming the AGN wind and the AGN jet
models. We demonstrate that, considering 50 hours of observations, CTA can be
effectively used to constrain the two different emission models, providing
important insight into the physics governing the acceleration of particles in
non-relativistic AGN-driven outflows. This analysis strongly motivates
observations of Seyfert and starburst galaxies with CTA in order to test source
population models of the extragalactic gamma-ray and neutrino backgrounds.
