The Fermi $gamma$-ray space telescope reported the observation of several Galactic supernova remnants recently, with the $gamma$-ray spectra well described by hadronic $pp$ collisions. The possible neutrino emissions from these Fermi detected supernova remnants are discussed in this work, assuming the hadronic origin of the $gamma$-ray emission. The muon event rates induced by the neutrinos from these supernova remnants on typical km$^3$ neutrino telescopes, such as the IceCube and the KM3NeT, are calculated. The results show that for most of these supernova remnants the neutrino signals are too weak to be detected by the on-going or up-coming neutrino experiment. Only for the TeV bright sources RX J1713.7-3946 and possibly W28 the neutrino signals can be comparable with the atmospheric background in the TeV region, if the protons can be accelerated to very high energies. The northern hemisphere based neutrino telescope might detect the neutrinos from these two sources.
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