  The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory is an
extensive air shower array located in Puebla, Mexico. The closest radio galaxy
within the HAWC field of view, M87, has been detected in very high energies. In
this work we report upper limits on the TeV {\gamma}-ray flux of the radio
galaxy M87. At a distance of 16 Mpc, M87 is a supergiant elliptical galaxy
located in the Virgo Cluster that has been observed from radio wavelengths to
TeV {\gamma}-rays. Although a single-zone synchrotron self-Compton model has
been successfully used to explain the spectral energy distribution of this
source up to a few GeV, the {\gamma}-ray spectrum at TeV has been interpreted
within different theoretical models. We discuss the implications of these upper
limits on the photo-hadronic interactions, as well as the number of neutrino
events expected in the IceCube neutrino telescope.
