In popular media, there is often a connection drawn between the advent of awareness in artificial agents and those same agents simultaneously achieving human or superhuman level intelligence. In this work, we explore the validity and potential application of this seemingly intuitive link between consciousness and intelligence. We do so by examining the cognitive abilities associated with three contemporary theories of conscious function: Global Workspace Theory (GWT), Information Generation Theory (IGT), and Attention Schema Theory (AST). We find that all three theories specifically relate conscious function to some aspect of domain-general intelligence in humans. With this insight, we turn to the field of Artificial Intelligence (AI) and find that, while still far from demonstrating general intelligence, many state-of-the-art deep learning methods have begun to incorporate key aspects of each of the three functional theories. Having identified this trend, we use the motivating example of mental time travel in humans to propose ways in which insights from each of the three theories may be combined into a single unified and implementable model. Given that it is made possible by cognitive abilities underlying each of the three functional theories, artificial agents capable of mental time travel would not only possess greater general intelligence than current approaches, but also be more consistent with our current understanding of the functional role of consciousness in humans, thus making it a promising near-term goal for AI research.