Procedural memory refers to skills acquired through practice and depends on cortico-striatal and cortico-cerebellar circuits. These circuits are typically affected in Parkinson's disease (PD), leading to impaired skill learning, including defective offline consolidation, early in the course of the disease. Evidence points to a role of slow oscillations (<4 Hz) during sleep for offline consolidation. However recent studies showed consolidation over the course of the day, suggesting that consolidation may arise during wakefulness, too. Here we investigate whether functional connectivity (FC) at rest after visuo-motor skill learning is associated with the extent of offline improvements in healthy controls and PD patients. Nineteen participants (9 PD, 10 healthy controls) performed a mirror-drawing task. High-density 156-channel resting state EEG was recorded before and immediately after training. Performance on the task was measured again 24 h later to test for offline consolidation. Delta-band (1–3.5 Hz) FC centered on the left parietal cortex after training predicted offline consolidation. Weak FC was observed in most healthy controls and associated with marked overnight improvement, while strong FC was observed in most PD patients and associated with weak offline consolidation or loss of the skill. These findings indicate that offline consolidation starts immediately after visuo-motor skill learning in brain regions and frequencies typically involved in sleep-related consolidation.