This extended abstract paper summarizes our ongoing research related to improving the dependability of DNN-based autonomous driving systems. Particularly, we address the problem of recognizing unexpected execution contexts with the purpose of predicting potential safety-critical misbehaviours. Our approach SelfOracle is based on a novel concept of self-assessment oracle, which monitors the DNN confidence at runtime, to predict unsupported driving scenarios in advance. SelfOracle uses autoencoder- and time series-based anomaly detection to reconstruct the driving scenarios seen by the car, and to determine the confidence boundary between normal and unsupported conditions. Our evaluation using three self-driving car models shows promising results against a diverse set of simulated anomalous driving contexts.