<p>In the present work, we theoretically investigate the optical bistability in a dimer consisting of two graphene-coated dielectric nanoparticles with a single molecule placed in the gap region. Assuming this system is exposed to an electromagnetic field, by solving Laplace’s equation in the quasi-static approximation, we obtain the local electric fields in different regions of the proposed system. The results show that the presence of molecule in the gap of dimer significantly affects the bistable behavior and leads to changes in the bistability thresholds and hysteresis loop compared to the dimer without the molecule. Furthermore, we explore the effects of nanoparticle asymmetry and the molecule dipole moment on the bistable response. We found that by increasing the degree of asymmetry, where the two nanoparticles differ in size, the bistability region will be increased and broadened. However, these findings may find practical potential applications in nanophotonic and optoelectronic devices.</p>