Eye movements, such as saccades, allow us to gather information about the environment and, in this way, can shape memory. In non-human primates, saccades are associated with the activity of grid cells in the entorhinal cortex. Grid cells are essential for spatial navigation, but whether saccade-based grid-like signals play a role in human memory formation is currently unclear. Here, human participants undergo functional magnetic resonance imaging and continuous eye gaze monitoring while studying scene images. Recognition memory is probed immediately thereafter. Results reveal saccade-based grid-like codes in the left entorhinal cortex that are specific to later remembered trials during study, a finding that we replicate with an independent data set. The grid-related effects are time-locked to activation increases in the frontal eye fields. Unexpectedly, lower saccade-based grid-like codes are associated with better subsequent recognition memory performance. Our findings suggest an entorhinal map of visual space that is timed with neural activity in oculomotor regions, and negatively associated with subsequent memory. Grid-like codes, entorhinal cortex, saccades, frontal eye fields (FEF), memory, functional magnetic resonance imaging (fMRI).