Reconstruction methods for multi-contrast MRI often employ a low-rank constraint to reconstruct images from highly undersampled data. For multi-echo gradient echo sequences such a constraint is hard to impose due off-resonance-induced oscillations of the time signals. In this work we show that spatio-temporal correlations can be exploited efficiently using locally low rank regularization. Based on this observation we develop a locally-low rank regularized reconstruction scheme and test it on a multi-echo gradient echo dataset of a human brain. In our tests the proposed method shows significantly improved image quality compared to regular compressed sensing reconstructions.