The combination of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) has been proposed as a tool to study brain dynamics with both high temporal and high spatial resolution. Multimodal imaging techniques rely on the assumption of a common neuronal source for the different recorded signals. In order to maximally exploit the combination of these techniques, one needs to understand the coupling (i.e., the relation) between electroencephalographic (EEG) and fMRI blood oxygen level-dependent (BOLD) signals. Recently, simultaneous EEG-fMRI measurements have been used to investigate the relation between the two signals. Previous attempts at the analysis of simultaneous EEG-fMRI data reported significant correlations between regional BOLD activations and modulation of both event-related potential (ERP) and oscillatory EEG power, mostly in the alpha but also in other frequency bands. Beyond the correlation of the two measured brain signals, the relevant issue we address here is the ability of predicting the signal in one modality using information from the other modality. Using multivariate machine learning-based regression, we show how it is possible to predict EEG power oscillations from simultaneously acquired fMRI data during an eyes-open/eyes-closed task using either the original channels or the underlying cortically distributed sources as the relevant EEG signal for the analysis of multimodal data.