The consolidation of declarative memories benefits from sleep. The neural mechanisms involved in sleep-dependent consolidation, however, are largely unknown. Here, we used a combination of functional magnetic resonance imaging, polysomnography and a face–location associative memory task to target neural connectivity of a face sensitive area during an afternoon nap. Fusiform connectivity was substantially greater during sleep stage 1 than in wake in a network extending from early visual areas bilaterally to the fusiform gyrus, ventrally and into the posterior parietal cortices, dorsally. In sleep stage 2, fusiform connectivity was found to be larger in the precuneus, bilateral middle temporal gyrus and medial prefrontal cortex. Specific functional connectivity increases observed during light sleep were positively correlated with memory performance for face–location associations. A distinction could be made between fusiform-medial prefrontal connectivity during sleep stage 1 and 2 that was positively correlated with retention of associations learned prior to sleep and fusiform-hippocampal connectivity during sleep stage 1 that was correlated with better acquisition of new associations learned after sleep. Our results suggest that fusiform-medial prefrontal connectivity during sleep has a stabilizing effect on recently learned associative memories, possibly due to the existence of a task-related schema that allows rapid consolidation of related information. Our data further indicate that sleep-dependent connectivity between the fusiform gyrus and hippocampus correlated with new learning after sleep. Thus, our study provides correlational evidence for the behavioral relevance of specific medial prefrontal and hippocampal interactions with the fusiform gyrus during light sleep.