The experience of inner speech is a common one. Such a dialogue accompanies the introspection of mental life and fulfills essential roles in human behavior, such as self-restructuring, self-regulation, and re-focusing on attentional resources. Although the underpinning of inner speech is mostly investigated in psychological and philosophical fields, the research in robotics generally does not address such a form of self-aware behavior. Existing models of inner speech inspire computational tools to provide a robot with this form of self-awareness. Here, the widespread psychological models of inner speech are reviewed, and a cognitive architecture for a robot implementing such a capability is outlined in a simplified setup.