The elastic scattering of 6,7Li+28Si reactions has been analyzed in the framework of the double folding optical model. Semi-microscopic folded potentials are generated based on the alpha (α)-cluster structure of the colliding nuclei. Successful reproduction of the observed angular distributions of the elastic scattering differential cross section and reaction cross sections has been obtained at different energies using the derived potentials. A microscopic folding approach based on the effective DDM3Y nucleon–nucleon interaction and the nuclear matter densities of the interacting nuclei is also considered.