  The hypothesis of a PeVatron in the Galactic Center, emerged with the recent
{\gamma}-ray measurements of H.E.S.S., motivates the search for neutrinos from
this source. The effect of {\gamma}-ray absorption is studied: at the energies
currently probed, the known background radiation fields lead to small effects,
whereas it is not possible to exclude large effects due to new IR radiation
fields near the very Center. Precise upper limits on neutrino fluxes are
derived and the underlying hypotheses are discussed. The expected number of
events for ANTARES, IceCube and KM3NeT, based on the H.E.S.S. measurements, are
calculated. It is shown that km3-class telescopes in the Northern hemisphere
have the potential of observing high-energy neutrinos from this important
astronomical object and can check the existence of a hadronic PeV galactic
accelerator.
