The reversible resistive switching in ZnO nanowire-based memristive devices is here discussed. Four configurations were studied: top electrode in Pt, with and without polymer coating (polyacrylic acid); top electrode in Cu, with and without the same polymer coating. All the tested devices showed a bipolar resistive switching behavior, with enhanced I-V non-linearity when coated with the polymer. While well-known physical mechanisms such as vacancy and ion-dominated conduction are clearly involved in resistive switching of ZnO nanowires, the coating with the polymer induces new features in the I-V characteristics, probably thanks to the modification of the surface states of ZnO nanowires. Thus, new memristive nanodevices with enhanced electrical features can be developed with such approach.