While extra-personal space is often erroneously considered as a unique entity, early neuropsychological studies report a dissociation between near and far space processing both in humans and in monkeys. Here, we use functional MRI in a naturalistic 3D environment to describe the non-human primate near and far space cortical networks. We describe the co-occurrence of two extended functional networks respectively dedicated to near and far space processing. Specifically, far space processing involves occipital, temporal, parietal, posterior cingulate as well as orbitofrontal regions not activated by near space, possibly subserving the processing of the shape and identity of objects. In contrast, near space processing involves temporal, parietal, prefrontal and premotor regions not activated by far space, possibly subserving the preparation of an arm/hand mediated action in this proximal space. Interestingly, this network also involves somatosensory regions, suggesting a cross-modal anticipation of touch by a nearby object. Last, we also describe cortical regions that process both far and near space with a preference for one or the other. This suggests a continuous encoding of relative distance to the body, in the form of a far-to-near gradient. We propose that these cortical gradients in space representation subserve the physically delineable peripersonal spaces described in numerous psychology and psychophysics studies.