People make inferences about the trustworthiness of others based on their observed gaze behaviour. Faces that consistently look towards a target location are rated as more trustworthy than those that look away from the target. Representations of trust are important for future interactions; yet little is known about how they are consolidated in long-term memory. Sleep facilitates memory consolidation for incidentally-learned information and may therefore support the retention of trust representations. We investigated the consolidation of trust inferences across periods of sleep or wakefulness. In addition, we employed a memory cueing procedure (targeted memory reactivation, TMR) in a bid to strengthen certain trust memories over others. We observed no difference in the retention of trust inferences following delays of sleep or wakefulness, and there was no effect of TMR in either condition. Interestingly, trust inferences remained stable one week after learning, irrespective of the initial post-learning delay. A second experiment showed that this implicit learning occurs despite participants’ being unable to explicitly recall the gaze behaviour of specific faces immediately after encoding. Together, these results suggest that gist-like, social inferences are formed at the time of learning without retaining the original episodic memory and thus do not benefit from offline consolidation through replay. We discuss our findings in the context of a novel framework whereby trust judgements reflect an efficient, powerful, and adaptable storage device for social information.