Eye tracking is handled as one of the key technologies for applications that assess and evaluate human attention, behavior, and biometrics, especially using gaze, pupillary, and blink behaviors. One of the challenges with regard to the social acceptance of eye tracking technology is however the preserving of sensitive and personal information. To tackle this challenge, we employ a privacy-preserving framework based on randomized encoding to train a Support Vector Regression model using synthetic eye images privately to estimate the human gaze. During the computation, none of the parties learn about the data or the result that any other party has. Furthermore, the party that trains the model cannot reconstruct pupil, blinks or visual scanpath. The experimental results show that our privacy-preserving framework is capable of working in real-time, with the same accuracy as compared to non-private version and could be extended to other eye tracking related problems.