Fetal and neonatal brain connectivity development is highly complex. Studies have shown that functional networks change dramatically during development. The purpose of the current study was to determine how the mean phase lag index (mPLI), a measure of functional connectivity (FC), assessed with electroencephalography (EEG), changes with postmenstrual age (PMA) during the early stages of brain development after birth. Neonates (N = 131) with PMA 27.6–45.3 weeks who underwent an EEG for a medical reason were retrospectively studied. For each recording, global FC was assessed by obtaining a whole-head average of all local PLI values (pairwise between sensor space EEG signals). Global FC results were consequently correlated with PMA values in seven frequency bands. Local results were obtained for the frequency band with the strongest global association. There was a strong negative correlation between mPLI and PMA in most frequency bands. The strongest association was found in the delta frequency band (R = −0.616, p < 0.001) which was therefore topographically explored; the strongest correlations were between pairs of electrodes with at least one electrode covering the central sulcus. Even in this heterogeneous group of neonates, global FC strongly reflects PMA. The decrease in PLI may reflect the process of segregation of specific brain regions with increasing PMA. This was mainly found in the central brain regions, in parallel with myelination of these areas during early development. In the future, there may be a role for PLI in detecting atypical FC maturation. Moreover, PLI could be used to develop biomarkers for brain maturation and expose segregation processes in the neonatal brain.