Directed connectivity between brain sources identified from scalp electroencephalography (EEG) can shed light on the brain’s information flows and provide a biomarker of neurological disorders. However, as volume conductance results in scalp activity being a mix of activities originating from multiple sources, the correct interpretation of their connectivity is a formidable challenge despite source localization being applied with some success. Traditional connectivity approaches rely on statistical assumptions that usually do not hold for EEG, calling for a model-free approach. We investigated several types of Artificial Neural Networks in estimating Directed Connectivity between Reconstructed EEG Sources and assessed their accuracy with respect to several ground truths. We show that a Long Short-Term Memory neural network with Non-Uniform Embedding yields the most promising results due to its relative robustness to differing dipole locations. We conclude that certain network architectures can compete with the already established methods for brain connectivity analysis.