The holographic dark energy models provide an alternative description of dark energy. These models are motivated by the possible application of the holographic principle to the dark energy problem. In this work, we present a theoretical study of the one parameter Li holographic dark energy and the two parameter Barrow holographic dark energy models using configuration entropy of the matter distribution in the universe. The configuration entropy rate exhibits a distinct minimum at a specific scale factor that corresponds to the epoch, beyond which dark energy takes a driving role in the accelerated expansion of the universe. We find that the location of the minimum and magnitude of the entropy rate at the minimum are sensitive to the parameters of the models. We find the best fit relations between these quantities and the parameters of each model. We propose that these relations can be used to constrain the parameters of the holographic dark energy models from future observations such as the SKA. Our study suggests that the signature of a large quantum gravitational effect on the future event horizon can be detected from measurements of the configuration entropy of the matter distribution at multiple redshifts.