The influence of a reflecting surface on the optical bistability in a nanoantenna array is investigated theoretically. The optical response of the array is modeled using a surface integral equation method developed for periodic structures, and the description of the Kerr effect is based on an analytical model. Different behaviors are observed when the distance between the nanoantenna array and the silver layer is changed. Indeed, a modification of the nanoantennas radiative properties permit to control important parameters of the nonlinear response such as the intensity threshold and the area of the hysteresis cycle. The results presented in this article demonstrate that a reflecting surface is a convenient and flexible tool for controlling the operating of nonlinear optical systems based on the Kerr effect.