Numerous studies in the literature have already shown the potential of biometrics on mobile devices for authentication purposes. However, it has been shown that, the learning processes associated to biometric systems might expose sensitive personal information about the subjects. This study proposes GaitPrivacyON, a novel mobile gait biometrics verification approach that provides accurate authentication results while preserving the sensitive information of the subject. It comprises two modules: i) a convolutional Autoencoder that transforms attributes of the biometric raw data, such as the gender or the activity being performed, into a new privacy-preserving representation; and ii) a mobile gait verification system based on the combination of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) with a Siamese architecture. The main advantage of GaitPrivacyON is that the first module (convolutional Autoencoder) is trained in an unsupervised way, without specifying the sensitive attributes of the subject to protect. The experimental results achieved using two popular databases (MotionSense and MobiAct) suggest the potential of GaitPrivacyON to significantly improve the privacy of the subject while keeping user authentication results higher than 99% Area Under the Curve (AUC). To the best of our knowledge, this is the first mobile gait verification approach that considers privacy-preserving methods trained in an unsupervised way.