Peri-hand space is the area surrounding the hand. Objects within this space may be subject to increased visuospatial perception, increased attentional prioritization, and slower attentional disengagement compared to more distal objects. This may result from kinesthetic and visual feedback about the location of the hand that projects from the reach and grasp networks of the dorsal visual stream back to occipital visual areas, which in turn, refines cortical visual processing that can subsequently guide skilled motor actions. Thus, we hypothesized that visual stimuli that afford action, which are known to potentiate activity in the dorsal visual stream, would be associated with greater alterations in visual processing when presented near the hand. To test this, participants held their right hand near or far from a touchscreen that presented a visual array containing a single target object that differed from 11 distractor objects by orientation only. The target objects and their accompanying distractors either strongly afforded grasping or did not. Participants identified the target among the distractors by reaching out and touching it with their left index finger while eye-tracking was used to measure visual search times, target recognition times, and search accuracy. The results failed to support the theory of enhanced visual processing of graspable objects near the hand as participants were faster at recognizing graspable compared to non-graspable targets, regardless of the position of the right hand. The results are discussed in relation to the idea that, in addition to potentiating appropriate motor responses, object affordances may also potentiate early visual processes necessary for object recognition.