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Quasielastic excitation functions for the 16,18 O + 60 Ni systems were measured at energies near and below the Coulomb barrier, at the backward angle θ LAB = 161 • . The corresponding quasielastic barrier distributions were derived. The data were compared with predictions from coupled channel calculations using a double-folding potential as a bare potential. For the 16 O-induced scattering, good agreement was obtained for the barrier distribution by using the projectile default nuclear matter diffuseness obtained from the São Paulo potential systematic, that is, 0.56 fm. However, for the 18 O-induced scattering, good agreement was obtained only when the projectile nuclear matter diffuseness was changed to 0.62 fm. Therefore, in this paper we show how near-barrier quasielastic scattering can be used as a sensitive tool to derive nuclear matter diffuseness.