Many studies have found that fixating or directing spatial attention to different regions can bias the perception of the Necker cube, but whether this effect of spatial attention is due to attended areas perceived as being closer have yet to be examined. This issue was directly investigated in this study. The stimulus used was the diamond stimulus, containing four occluders and four moving lines that can be perceived as coherent or separate motions. The results of Experiment 1 show that coherent motion was perceived more often under the attending-to-occluders condition than under the attending-to-moving-lines condition, indicating that spatial attention can bias multistable perception. The results of Experiment 2 show that the mean probability of reporting lines behind occluders in small binocular disparities was significantly higher under the attending-to-occluders condition than under the attending-to-lines condition, indicating that spatial attention can make attended areas look slightly closer. The results of Experiments 3 and 4 show that the effect of spatial attention on biasing multistable perception was weakened when there were binocular or monocular depth cues to define the depth relationship between the occluders and the lines. These results are all consistent with the notion that spatial attention can bias multistable perception through affecting depth perception, making attended areas look closer.