Gaze cues serve an important role in facilitating human conversations and are generally considered to be one of the most important non-verbal cues. Gaze cues are used to manage turn-taking, coordinate joint attention, regulate intimacy, and signal cognitive effort. In particular, it is well established that gaze aversion is used in conversations to avoid prolonged periods of mutual gaze. Given the numerous functions of gaze cues, there has been extensive work on modelling these cues in social robots. Researchers have also tried to identify the impact of robot gaze on human participants. However, the influence of robot gaze behavior on human gaze behavior has been less explored. We conducted a within-subjects user study (N = 33) to verify if a robot’s gaze aversion influenced human gaze aversion behavior. Our results show that participants tend to avert their gaze more when the robot keeps staring at them as compared to when the robot exhibits well-timed gaze aversions. We interpret our findings in terms of intimacy regulation: humans try to compensate for the robot’s lack of gaze aversion.