The central region of our Galaxy is a very peculiar environment, containing magnetic fields in excess of 100 mG and gas densities reaching 104cm-3. This region was observed as a strong source of GeV and TeVs gammas, what suggests that a mechanism of proton-neutron conversion could be taking place therein. We propose that the Galactic Center must also be a source of EeV neutrons due to the conversion of ultra high energy cosmic ray protons into neutrons via p-p interactions inside this region. This scenario should be falsifiable by the Pierre Auger Observatory after a few years of full exposure.