Mutual information (MI) is a promising candidate measure for the assessment and optimization of localization systems, as it captures nonlinear dependencies between random variables. However, the high cost of computing MI, especially for high-dimensional problems, prohibits its application for many real-world localization systems. We evaluate an algorithm from a new class of neural MI estimators called Mutual Information Neural Estimation (MINE) to approximate the MI between the set of feasible user element (UE) locations and the corresponding set of measurements from said UE locations used for positioning. We apply this estimator to a simulated multilateration (MLAT) system, where the true MI for benchmarking can be approximated by Monte Carlo simulation. The estimator is experimentally evaluated w.r.t. its convergence and consistency and we investigate the usefulness of MI for assessing simple MLAT systems.