In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment.