  A crucial process in Galactic cosmic-ray (CR) transport is the spatial
diffusion due to the interaction with the interstellar turbulent magnetic
field. Usually, CR diffusion is assumed to be uniform and isotropic all across
the Galaxy. However, this picture is clearly inaccurate: Several data-driven
and theoretical arguments, as well as dedicated numerical simulations, show
that diffusion exhibits highly anisotropic properties with respect to the
direction of a background (ordered) magnetic field (i.e., parallel or
perpendicular to it). In this paper we focus on a recently discovered anomaly
in the hadronic CR spectrum inferred by the Fermi-LAT gamma-ray data at
different positions in the Galaxy, i.e. the progressive hardening of the proton
slope at low Galactocentric radii. We propose the idea that this feature can be
interpreted as a signature of anisotropic diffusion in the complex Galactic
magnetic field: In particular, the harder slope in the inner Galaxy is due, in
our scenario, to the parallel diffusive escape along the poloidal component of
the large-scale, regular, magnetic field. We implement this idea in a numerical
framework, based on the DRAGON code, and perform detailed numerical tests on
the accuracy of our setup. We discuss how the effect proposed depends on the
relevant free parameters involved. Based on low-energy extrapolation of the few
focused numerical simulations aimed at determining the scalings of the
anisotropic diffusion coefficients, we finally present a set of plausible
models that reproduce the behavior of the CR proton slopes inferred by
gamma-ray data.
