Entropic attraction between anisotropic nanoparticles in nonadsorbing polymer solutions is significantly greater than that between nanospheres. In this study, depletion attraction between two solvophilic nanodiscs and the aggregation behavior of a nanodisc suspension are explored by dissipative particle dynamics. The depletion force due to polymer addition is proportional to the product of the osmotic pressure and the area of the nanodisc, even for concentrated polymer solutions. For a suspension of nanodiscs, three possible equilibrium states are observed upon polymer addition: dispersion, pretransition, and phase separation. By varying nanodisc concentration (phi(D)) and polymer concentration (phi(P)), the phase diagram is obtained. Dispersion exists for small phi(D) and phi(P). As phi(D) exceeds critical aggregation concentration, finite sized clusters are mainly formed with columnar structure in the pretransition regime, similar to micellization associated with typical surfactants. The mean size of columnar clusters seems to grow with phi(1/2)(D) and phi(P). For high enough phi(D) and phi(P), finite sized clusters vanish and phase separation appears. The nanodisc-rich phase is formed by a bundle of columns or a pack of columns owing to face-to-side and side-to-side depletion attractions.