The quasi-elastic excitation function for the 17 O + 64 Zn system was measured at energies near and below the Coulomb barrier, at the backward angle θ lab = 161 • . The corresponding quasi-elastic barrier distribution was derived. The excitation function for the neutron stripping reactions was also measured, at the same angle and energies, and the experimental values of the spectroscopic factors were deduced by fitting the data. A reasonably good agreement was obtained between the experimental quasi-elastic barrier distribution with the coupled-channel calculations including a very large number of channels. Of the channels investigated, three dominated the coupling matrix: two inelastic channels, 64 Zn(2 + 1 ) and 17 O(1/2 + ), and one-neutron transfer channel, particularly the first one. On the other hand, a very good agreement is obtained when we use a nuclear diffuseness for the 17 O nucleus larger than the one for 16 O. We verify that quasi-elastic barrier distribution is a sensitive tool for determining nuclear matter diffuseness.