Binocular rivalry, a phenomenon in which perception switches between stimuli that are presented to different eyes, is commonly employed to study consciousness-related effects in humans and non-human primates. As mice are becoming increasingly popular as model organisms to study visual perception, recent studies have started to investigate the neuronal underpinnings of mouse binocular vision. However, to our knowledge, no systematic investigation of whether mice experience binocular rivalry-like perception when presented with binocularly conflicting stimuli exists. Here, we recorded neuronal activity in mouse visual cortex with 2-photon imaging while mice were passively viewing binocularly conflicting stimuli. We present first, preliminary results suggesting that presenting a flashing stimulus in binocular conflict with a grating suppresses the otherwise orientation-tuned responses of roughly a third of neurons in mouse visual areas. Notably, similar response suppression in visual areas has been reported when a stimulus is suppressed from awareness during binocular rivalry in primates. While this finding is not direct evidence for the occurrence of binocular rivalry in mouse perception per se, this shared mechanism of binocular conflict processing in mice and primates calls for further investigation of the nature of mouse perception during binocular conflict.