Recently, a diffuse γ-rays emission in the energy range 1-100 GeV has been detected around M31, that extends up to 120-200 kpc from its center. Such extended emission is difficult to be explained in the typical scenario of cosmic rays produced in the galactic disk or in the galactic center (GC) and diffusing in the galactic halo. We show that a cosmic ray origin, either hadronic or leptonic, of the emission is viable if non-standard cosmic ray transport scenarios are considered, or if particles are accelerated directly in the galactic halo (in situ acceleration). The cosmic ray halo can be powered by the accretion of intergalactic gas or by the activity of galaxy’s central black hole. If giant cosmic ray halos are common around galaxies, the interactions of cosmic ray protons and nuclei with the circumgalactic gas surrounding Milky Way could explain the isotropic diffuse flux of neutrinos observed by Icecube.