Spoofing of the GNSS signals presents continuous threat to the users of safety of life applications due to unaware use of false signals in generating position and timing solution. Among numerous anti-spoofing techniques applied at different stages of the signal processing, we present approach of monitoring the cross-correlation of multiple GNSS observables and measurements as an input for supervised machine learning based approach to detect potentially spoofed GNSS signals. Both synthetic, generated in laboratory, and real-world spoofing datasets were used for verification and validation of the supervised machine learning algorithms for detection of the GNSS spoofing.