This paper discusses the possibility of the phenomenon of empathy between humans and robots, starting from what happens during their eye contact. First, it is shown, through the most relevant results of HRI studies on this matter, what are the most important effects of the robot gaze on human emotions and behaviour. Secondly, these effects are compared to what happens during the phenomenon of empathy between humans, taking inspiration from the studies of Edmund Husserl and Edith Stein. Finally, similarities and differences between human-human and human-robot empathy are conceptualized through Merleau-Ponty’s idea of flesh, which is the extended bodily element of the world. If there is a common concept of body, including both machine-bodies and living bodies, then a transcorporeal analogy takes place, thus explaining why the phenomenon of empathy occurs both in human-human and human-robot interactions.