Successful application of finite control set model predictive control (FCS-MPC) strategies with long prediction horizon depends on the careful design of the optimization algorithm. The conventional method involves transforming the problem to an equivalent box-constrained integer least-squares (BILS) formulation that can be solved with branch-and-bound techniques such as the sphere decoding algorithm (SDA). In this work, it is proposed to define an artificial neural network (ANN) to replace the SDA, avoiding its inherent computational variability. Similarly to practical applications of the SDA, the ANN finds an approximate solution of the underlying optimization problem. In contrast, the main benefit of the proposed approach is that it can be implemented in a low-cost microprocessing platform, greatly improving the performance in terms of resources in comparison with other advanced techniques roposed in the literature.