Ultra-Luminous Infrared Galaxies (ULIRGs) are the most luminous objects in the infrared sky. With infrared luminosities exceeding $10^{12}$ solar luminosities, ULIRGs contain strong star formation regions which could power hadronic acceleration. Moreover, a significant fraction of ULIRGs have been found to host Active Galactic Nuclei, which could also be a source of hadronic acceleration. Furthermore, such high infrared luminosities indicate that large amounts of dust are present in these objects. In the presence of hadronic acceleration, this dust not only represents an excellent target for high-energy neutrino production through the \textit{pp}-channel, but it could also attenuate a significant fraction of the gamma rays that are produced in this process. This could relieve the apparent tension between the diffuse IceCube neutrino flux and the diffuse gamma-ray flux measured by \textit{Fermi}-LAT. We present our source selection criteria and IceCube sensitivities in view of a search for high-energy neutrinos from these so far unexplored objects.