The neural basis of absolute pitch (AP), the ability to effortlessly identify a musical tone without an external reference, is poorly understood. One of the key questions is whether perceptual or cognitive processes underlie the phenomenon as both sensory and higher-order brain regions have been associated with AP. To integrate the perceptual and cognitive views on AP, here, we investigated joint contributions of sensory and higher-order brain regions to AP resting-state networks. We performed a comprehensive functional network analysis of source-level EEG in a large sample of AP musicians (n = 54) and non-AP musicians (n = 51), adopting two analysis approaches: First, we applied an ROI-based analysis to examine the connectivity between the auditory cortex and the dorsolateral prefrontal cortex (DLPFC) using several established functional connectivity measures. This analysis is a replication of a previous study which reported increased connectivity between these two regions in AP musicians. Second, we performed a whole-brain network-based analysis on the same functional connectivity measures to gain a more complete picture of the brain regions involved in a possibly large-scale network supporting AP ability. In our sample, the ROI-based analysis did not provide evidence for an AP-specific connectivity increase between the auditory cortex and the DLPFC. The whole-brain analysis revealed three networks with increased connectivity in AP musicians comprising nodes in frontal, temporal, subcortical, and occipital areas. Commonalities of the networks were found in both sensory and higher-order brain regions of the perisylvian area. Further research will be needed to confirm these exploratory results.