Recent work investigated the influence of exogenous attention on initial percept dominance at the onset of binocular rivalry. It was reported that cueing attention to one of two binocularly presented transparent stimuli immediately prior to rivalrous viewing provided the cued stimulus with a competitive advantage in subsequent binocular rivalry. This effect was independent of the eye containing the cued stimulus during the rivalry phase. In this recent work, the attention cue was always presented to both eyes. This leaves unclear the extent to which cueing affects binocular and/or monocular stimulus representations. To disambiguate this issue, we compared the cueing strength when the cue was presented ipsi-, contra- or bi-laterally with respect to the eye containing the cued stimulus during subsequent binocular rivalry. Besides replicating previous findings, we found that stimulus cueing readily transfers across eyes, suggesting that binocular mechanisms mediate exogenous attention effects on dominance selection at the onset of binocular rivalry.