Human faces can convey socially relevant information in various ways. Since the early detection of such information is crucial in social contexts, socially meaningful information might also have privileged access to awareness. This is indeed suggested by previous research using faces with emotional expressions. However, the social relevance of emotional faces is confounded with their physical stimulus characteristics. Here, we sought to overcome this problem by manipulating the relevance of face stimuli through classical conditioning: Participants had to learn the association between different face exemplars and high or low amounts of positive and negative monetary outcomes. Before and after the conditioning procedure, the time these faces needed to enter awareness was probed using continuous flash suppression, a variant of binocular rivalry. While participants successfully learned the association between the face stimuli and the respective monetary outcomes, faces with a high monetary value did not enter visual awareness faster than faces with a low monetary value after conditioning, neither for rewarding nor for aversive outcomes. Our results tentatively suggest that behaviorally relevant faces do not have privileged access to awareness when the assessment of the faces' relevance is dependent on the processing of face identity, as this requires complex stimulus processing that is likely limited at pre-conscious stages.