We investigate some non-perturbative models for Quantum Chromodynamics (QCD) with the purpose of testing its validity in the perturbative region of nuclear interaction and to explore its behavior in the infrared region. In particular, we focus on the calculations and analysis of the potentials between supermassive quarks and antiquarks, since this observable might reveal the appearance of confinement properties in non-perturbative models through a linear growth at large and intermediate distances. We calculate the potentials associated with the massive Gluon, Gribov-Zwanziger and Gribov-Zwanziger Refined models at tree level for the non-relativistic case. In addition, we have included the flux of the Renormalization Group in the QCD coupling constant, which allowed us to study the energy-scale dependence of the parameters of the potentials. Our results indicate that, in the tree-level approximation, all potentials we have obtained can reproduce the perturbative result at high energies and some of them bring significant non-perturbative corrections.