Biomedical applications based on superparamagnetic nanoparticles injected in vivo may be affected by the cellular uptake of these nanoparticles. Living cells indeed capture and internalize nanoparticles, concentrating them into intracellular vesicles called lysosomes. As a consequence, nanoparticles interact magnetically with each other, modifying their magnetic properties. The effects of cellular uptake can be observed on the temperature dependence of zero-field cooled (ZFC) magnetization, which is known to be sensitive to magnetic interactions. In this paper, a theoretical model is proposed to account for weak magnetic interactions between nanoparticles aggregated into spherical compartments. This model suggests a new interpretation of the maximum of the ZFC curve, uncorrelated with the nanoparticle relaxation time but with the extent of interaction effects. It focuses on the local field felt by each nanoparticle, which is the sum of the applied magnetic field and the field created by all the other nanoparticles. For the considered organization of nanoparticles, only the field created by touching neighbors has to be taken into account, setting up the local nanoparticle volume fraction as the unique parameter of the model. This parameter relates the global magnetization measurements to the local distribution of nanoparticles in cells and tissues or in other complex media with aggregated organization.