Three-phase motors are commonly adopted in several industrial contexts and their failures can result in costly downtime causing undesired service outages; this way, motor diagnostics is an issue that assumes great importance. To prevent their failures and timely face the considered service outages, a non-invasive method to identify electrical and mechanical faults in three-phase asynchronous electric motors is proposed in the paper. In particular, a measurement strategy along with a machine learning algorithm based on Artificial Neural Network is exploited to properly classify failures. In particular, digitized current samples of each motor phase are first processed by means of FFT and PSD in order to estimate the associated spectrum. Suitable features (in terms of frequency and amplitude of the spectral components) are then singled out to either train or feed a neural network acting as a classifier. The method is preliminary validated on a set of 28 electric motors, and its performance is compared with common state-of-art machine learning techniques. The obtained results show that the proposed methodology is able to reach accuracy levels greater than 98\% in identifying anomalous conditions of three-phase asynchronous motors.