The elastic and inelastic differential cross-sections of 32S on 28Si at incident energies of 77, 90, 97.09, 120, and 135 MeV were analyzed. The first 2+ excitation state in both nuclei as well as the [2+, 2+] mutual excitation were studied. The calculations were performed using double folding model. Three different potentials are used: the phenomenological Woods–Saxon double-folding cluster, in addition to the density-independent M3Y potential, which is considered for comparison. The imaginary potential part for the three potentials used was taken in the Woods-Saxon form. The influence of the inelastic channel on the elastic channel was investigated using the coupled channel method. Reasonable agreement for the considered experimental data for elastic and inelastic scattering was attained using the three generated potentials. The results of the cluster models show better agreement with the data than the other theoretical models. The total reaction and inelastic cross sections for low-lying excited states were extracted. The fitted deformation parameters for the transition potentials are also provided.