A large variety of nanoparticles hold extraordinary promise for practical applications in catalysis, materials science, medicine, and so on. It is, however, necessary to assemble them into supramolecular aggregates with desired structural properties. In this work we explore the self-assembly of spherical nanoparticles induced by interactions that, due to entropic effects, may become anisotropic. The spherical nanoparticles considered attract each other via square-well potentials, mimicking dispersive interactions. To induce anisotropic effects, short polymer brushes are bound to the nanoparticles but only on the equatorial plane. The brushes are treated as tangent-hard-sphere chains. Nanoparticles with such morphology could be synthesized experimentally. Monte Carlo calculations are conducted to assess the properties of the self-assembled nanostructures as a function of the length of the brushes and of the depth of the particle–particle square-well potential. Our results indicate that for strongly attractive particle–particle interactions it is possible to obtain supramolecular spherulites (employing short brushes) or uniform dispersions (using long brushes). At some intermediate lengths of the polymer brushes, the formation of one-dimensional wires occurs. Our results are useful for designing responsive nanoparticles that reversibly assemble yielding uniform dispersions, nanowires, or spherulites depending on the solution conditions.