Stroke often leads to permanent impairment in motor function. Accurate and quantitative prognosis of potential motor recovery before rehabilitation intervention can help healthcare centers improve resources organization and enable individualized intervention. The context of this paper investigated the potential of using electroencephalography (EEG) functional connectivity (FC) measures as biomarkers for assessing and prognosing improvement of Fugl-Meyer Assessment in upper extremity motor function (ΔFMU) among participants with chronic stroke. EEG data from resting and motor imagery task were recorded from 13 participants with chronic stroke. Three functional connectivity methods, which were Pearson correlation measure (PCM), weighted Phase Lag Index (wPLI) and phase synchronization index (PSI), were investigated, under three regions of interest (inter-hemispheric, intra-hemispheric, and whole-brain), in two statues (resting and motor imagery), with 15 refined center frequencies. We applied correlation analysis to identify the optimal center frequencies and pairs of synchronized channels that were consistently associated with ΔFMU. Predictive models were generated using regression analysis algorithms based on optimized center frequencies and channel pairs identified from the proposed analysis method, with leave-one-out cross-validation. We found that PSI in the Alpha band (with center frequency of 9Hz) was the most sensitive FC measures for prognosing motor recovery. Strong and significant correlations were identified between the predictions and actual ΔFMU scores both in the resting state (R2=0.79, P<0.001, N=13) and motor imagery (R2=0.65, P<0.001, N=13). Our results suggested that EEG connectivity measured with PSI in resting state could be a promising biomarker for quantifying motor recovery before motor rehabilitation intervention.