Spatial attention allows us to selectively process information within a certain location in space. Despite the vast literature on spatial attention, the effect of cognitive load on spatial processing is still not fully understood. In this study we added cognitive load to a spatial processing task, so as to see whether it would differentially impact upon the processing of visual information in the left versus the right hemispace. The main paradigm consisted of a detection task that was performed during the maintenance interval of a verbal working memory task. We found that increasing cognitive working memory load had a more negative impact on detecting targets presented on the left side compared to those on the right side. The strength of the load effect correlated with the strength of the interaction on an individual level. The implications of an asymmetric attentional bias with a relative disadvantage for the left (vs the right) hemispace under high verbal working memory (WM) load are discussed.