The entangling properties of models of classical gravity interacting with quantum matter (i.e., hybrid models of gravity) are investigated in the context of the experimental proposals to detect gravitationally induced entanglement. We prove that entanglement generation can indeed take place within these models, and characterize it quantitatively. We identify the root of entanglement generation in these models in the presence of some underlying nonlocality of the theories. Nonetheless, by focusing in particular on the Diósi-Penrose model for two gravitationally interacting masses, we show that entanglement-based experiments have the potential to either falsify the model entirely or constrain the free parameter of the model R0 up to values 6 orders of magnitude above the current state of the art.