This work proposes an innovative people-aware navigation for telepresence robots in a populated environment based on the estimated inclination of people to interact and the context information. The main novelty of the proposed people-aware shared intelligence is the ability to fuse the remote operator’s commands with the probability of person-robot interaction—from both the operator driving the robot and the people around it—and translate it into semi-autonomous approaching and avoiding behaviors that are not coded a priori but rather dynamically emerge according to the current context-awareness. Experiments involved 45 healthy participants who evaluated the proposed approach on a real robot. Three conditions have been tested: (a) the new people-aware shared intelligence; (b) a shared intelligence system integrated with the standard ROS social navigation layers and; (c) a direct teleoperation (i.e., no robot’s intelligence). Results from our people-aware shared intelligence system have shown that the robot’s social behaviors were in line with the expectations of the participants in terms of comfort, naturalness, and sociability and coherent with the findings from previous studies. Furthermore, the proposed system has facilitated the social interaction between the remote operator and the surrounding people, making the robot more proactive and without affecting navigation performance.