Simultaneous EEG-fMRI recordings are increasingly used to investigate brain activity by leveraging the complementary high spatial and high temporal resolution of fMRI and EEG signals respectively. It remains unclear, however, to what degree these two imaging modalities capture shared information about neural activity. Here, we investigate whether it is possible to predict both task-evoked and spontaneous fMRI signals of motor brain networks from EEG time-varying spectral power using interpretable models trained for individual subjects with Sparse Group Lasso regularization. Critically, we test the trained models on data acquired from each subject on a different day and obtain statistical validation by comparison with appropriate null models as well as the conventional EEG sensorimotor rhythm. We find significant prediction results in most subjects, although less frequently for resting-state compared to task-based conditions. Furthermore, we interpret the model learned parameters to understand representations of EEG-fMRI coupling in terms of predictive EEG channels, frequencies, and haemodynamic delays. In conclusion, our work provides evidence of the ability to predict fMRI motor brain activity from EEG recordings alone across different days, in both task-evoked and spontaneous conditions, with statistical significance in individual subjects. These results present great potential for translation to EEG neurofeedback applications.