Background: The nuclear structure of colliding nuclei is known to influence the fusion process. Couplings of the relative motion to nuclear shape deformations and vibrations lead to an enhancement of the sub-barrier fusion cross section in comparison with the predictions of one-dimensional barrier penetration models. This enhancement is explained by coupled-channels calculations including these couplings. The sub-barrier fusion cross section is also affected by nucleon transfer channels between the colliding nuclei. Purpose: The aim of the present experiment is to investigate the influence of the projectile and target nuclear structures on the fusion cross sections in the Ca-40 + Ni-58 and Ca-40 + Ni-64 systems. Methods: The experimental and theoretical fusion excitation functions as well as the barrier distributions were compared for these two systems. Coupled-channels calculations were performed using the CCFULL code. Results: Good agreement was found between the measured and calculated fusion cross sections for the Ca-40 + Ni-58 system. The situation is different for the Ca-40 + Ni-64 system where the coupled-channels calculations with no nucleon transfer clearly underestimate the fusion cross sections below the Coulomb barrier. The fusion excitation function was, however, well reproduced at low and high energies by including the coupling to the neutron pair-transfer channel in the calculations. Conclusions: The nuclear structure of the colliding nuclei influences the fusion cross sections below the Coulomb barrier for both Ca-40 + Ni-58,Ni-64 systems. Moreover, we highlighted the effect of the neutron pair-transfer channel on the fusion cross sections in Ca-40 + Ni-64.