Classical liquid activity coefficient models (LM), such as the NRTL model, fail near the critical point of the liquid-liquid equilibrium (LLE), unless a highly nonlinear temperature dependency is introduced for the molecular interaction parameters. In this work, we propose an approach to predict the LLE data near the critical point using data away from the critical region based on the global renormalization group theory (GRGT). In particular, we propose a non-empirical approach to determine the GRGT parameters, thus does not rely on experimental data. The performance of our method is examined with the NRTL model using 21 binary mixtures. Our results show that the predictive approach proposed in this work reduces the error in the critical solution temperatures by about 50% when compared to the classical NRTL model using linear temperature dependent interaction parameters.