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It was previously shown that beta oscillations of local field potentials in the arm area of the primary motor cortex (MI) of nonhuman primates propagate as travelling waves across MI of monkeys during movement preparation and execution and are believed to subserve cortical information transfer. To investigate the information transfer and its change over time at the single-cell level, we analyzed simultaneously recorded multiple MI neural spike trains of a monkey using a Granger causality measure for point process models before and after visual cues instructing the onset of reaching movements. In this analysis, we found that more pairs of neurons showed information transfer between them after appearances of upcoming movement targets than before, and the directions of the information transfer across neurons in MI were coincident with the directions of the propagating waves. These results suggest that the neuron pairs identified in the current study are the candidates of neurons that travel with spatiotemporal dynamics of beta oscillations in the MI.