The phenomenon of resistive switching is based on nanoscale changes in the electrical properties of the interface. In the present study, conductive atomic force microscope based nanoscale measurements of copper oxide (CuO)-multilayer graphene (MLG) hybrid interface based devices have been carried out to understand changes in the electrical properties during resistive switching of the Ti–CuO/MLG-Cu memory cells having different dimensions fabricated on the same substrate using stencil lithography technique. The dependence of resistive switching characteristics in LRS and HRS and current level of the conductive filaments (CF) on the electrode area have been studied. As the device dimension is reduced, the filamentary contribution is enhanced in comparison to the background contribution, resulting in an increase in the current density ratio between LRS and HRS. It is also observed that as the device dimension is decreased from 150 to 25 μm, the filament size decreases from 95 nm to 20 nm, respectively, which causes a decrease in the reset current and reset voltage. The results of the nanoscale CAFM measurements have shown a good correlation with the switching parameters obtained by the macroscale pad I–V measurements, thereby, suggesting the origin of resistive switching is due to the formation and rupture of an entity called filament, whose dimension is in nanorange. It is observed that changes in the electrical properties of the overall interface layer along with changes in the electrical conductivity of these filaments contribute towards resistive switching phenomenon. This study suggests that a significant reduction of reset current can be achieved by decreasing the memory device dimensions.