Gallium telluride presents interesting properties for applications in optoelectronic devices, such as solar panels and radiation detectors. These applications, however, have been hindered due to the low mobility of charge carriers and short lifetime of photoexcitations in this material. In this work we propose that these limitations could be overcome by van der Waals heterostructures of recently exfoliated GaTe monolayers and graphene sheets, combining the high photoabsorption of the former with the ballistic transport of the latter. Our analysis indicates that such structures have a binding energy greater than that of graphene bilayers and that the band offset is such that transfer of photoexcited electrons from GaTe to graphene should be spontaneous. To investigate the consequences of the relative position of graphene's Dirac cone with the band edges of the photon absorber, we propose two hypothetical new materials with the same atomic arrangement as GaTe: InTe and TlTe. Thermodynamic and dynamical analyses indicate that monolayers of these crystals, which should also present high photoresponsivity, are stable. Specifically for the case of TlTe we found that the band edges should coincide with graphene's Dirac cone in the brillouin zone, resulting in optimal transfer of photoexcited carriers.