We explore the possibility that high energy astrophysical neutrinos can interact with the dark matter on their way to Earth. Keeping in mind that new physics might leave its signature at such energies, we have considered all possible topologies for effective interactions between neutrino and dark matter. Building models, that give rise to a significant flux suppression of astrophysical neutrinos at Earth, is rather difficult. We present a Z -mediated model in this context. Encompassing a large variety of models, a wide range of dark matter masses from 10 −21 eV up to a TeV, this study aims at highlighting the challenges one encounters in such a model building endeavour after satisfying various cosmological constraints, collider search limits and electroweak precision measurements. *