Processing spatial configuration is a fundamental requirement for object recognition. Using fMRI, the neural basis underlying this ability was examined while human participants viewed possible and visually similar, but spatially impossible, objects presented for either long or short exposure duration. Response profiles in object-selective cortical regions exhibited sensitivity to object possibility, but only for the long exposure duration. Contrary, functional connectivity, indexed by the pairwise correlations between activation profiles across ROIs, revealed sensitivity to possibility, evident in enhanced correlations for impossible compared with possible objects. Such sensitivity was found even following a brief exposure duration, which allowed only minimal awareness of possibility. Importantly, this sensitivity was correlated with participants' general spatial ability as assessed by an independent neuropsychological test. These results suggest that the visual system is highly susceptible to objects' 3-D structural information even with minimal perceptual awareness. Such sensitivity is captured at the level of functional connectivity between object-selective regions, rather than the absolute level of within-region activity, implicating the role of interregional synchronization in the representation of objects' 3-D structure.