We appraise the capability of the Hartree-Fock approximation to reproduce the optical potential in the relativistic treatment. For this purpose we consider a variety of Lagrangian densities and study in detail the impact of different parameters, which may influence the optical potential. In general one can conclude that the energy dependence of the relativistic Hartree-Fock approximation is too weak, so that an agreement with experimental fits is only possible in certain energy windows. For comparison we also give some results for the Hartree approximation.