Global Navigation Satellite System (GNSS) signals are subject to different kinds of events causing significant errors in positioning. This work explores the application of Machine Learning (ML) methods of anomaly detection applied to GNSS receiver signals. More specifically, our study focuses on multipath contamination, using samples of the correlator output signal. The GPS L1 C/A signal data is used and sourced directly from the correlator output. To extract the important features and patterns from such data, we use deep convolutional neural networks (CNN), which have proven to be efficient in image analysis in particular. To take advantage of CNN, the correlator output signal is mapped as a 2D input image and fed to the convolutional layers of a neural network. The network automatically extracts the relevant features from the input samples and proceeds with the multipath detection. We train the CNN using synthetic signals. To optimize the model architecture with respect to the GNSS correlator complexity, the evaluation of the CNN performance is done as a function of the number of correlator output points.