  The recent progress made in Galactic gamma-ray astronomy using the High
Energy Stereoskopic System (H.E.S.S.) instrument provides for the first time a
population of Galactic TeV gamma-rays, and hence potential neutrino sources,
for which the neutrino flux can be estimated. Using the energy spectra and
source morphologies measured by H.E.S.S., together with new parameterisations
of pion production and decay in hadronic interactions, we estimate the signal
and background rates expected for these sources in a first-generation water
Cherenkov detector (ANTARES) and a next-generation neutrino telescope in the
Mediterranean Sea, KM3NeT, with an instrumented volume of 1 km^3. We find that
the brightest gamma-ray sources produce neutrino rates above 1 TeV, comparable
to the background from atmospheric neutrinos. The expected event rates of the
brightest sources in the ANTARES detector make a detection unlikely. However,
for a 1 km^3 KM3NeT detector, event rates of a few neutrinos per year from
these sources are expected, and the detection of individual sources seems
possible. Although generally these estimates should be taken as flux upper
limits, we discuss the conditions and type of gamma-ray sources for which the
neutrino flux predictions can be considered robust.
