Controlling cell interactions and how they form aggregates represents one of the main challenges in the cellular engineering field, especially when dealing with emerging 3D bioprinting applications. In vivo cells are known for their self-assembling capability at microscales into complex functional configurations such as spheroids and organoids. However, in vivo experimentation has failed to find the optimal conditions to recreate complex heterogeneous architectures, cell-cell, and extracellular matrix (ECM) in vivo interactions. This work is therefore dedicated to studying in silico interactions of spheroids embedded with magnetic nanoparticles. The main goal was to identify the key parameters responsible for forming complex 3D architectures in a controlled manner by applying magnetic fields. The obtained results showed that magnetized spheroids fuse to each other quite rapidly by the action of the applied magnetic fields. The fusion process agreed well with previous reports for unmagnetized spheroids; however, the model should be refined further by experimental testing to calibrate the fusion times. Despite the limitations, the presented approach confirms that the 3D assembly of cell aggregates is attainable through controlled magnetic fields gradients. This is useful to enable emerging applications in tissue engineering and 3D bioprinting that require the assembly of 3D living architectures.