Inner Speech is an essential but also elusive human psychological process\nwhich refers to an everyday covert internal conversation with oneself. We argue\nthat programming a robot with an overt self-talk system, which simulates human\ninner speech, might enhance human trust by improving robot transparency and\nanthropomorphism. For this reasons, this work aims to investigate if robot's\ninner speech, here intended as overt self-talk, affects human trust and\nanthropomorphism when human and robot cooperate. A group of participants was\nengaged in collaboration with the robot. During cooperation, the robot talks to\nitself. To evaluate if the robot's inner speech influences human trust, two\nquestionnaires were administered to each participant before (pre-test) and\nafter (post-test) the cooperative session with the robot. Preliminary results\nevidenced differences between the answers of participants in the pre-test and\npost-test assessment, suggesting that robot's inner speech influences human\ntrust. Indeed, participant's levels of trust and perception of robot\nanthropomorphic features increase after the experimental interaction with the\nrobot.\n