Grid cells in the entorhinal cortex have been identified to encode an animal’s position in space, but have been hypothesized to play a more fundamental role in mental operations. A prerequisite for this is that they can be activated in the absence of movement. Here, we investigated whether firing fields of entorhinal cells are activated by movements of covert attention, in the absence of any physical movement. For the study, we recorded the neuronal activity of 141 neurons in the entorhinal cortex of two rhesus macaque monkeys performing a covert attention tracking task. The results reveal that movement of covert attention, without any physical movement, also elicits spatial receptive fields with a triangular tiling of the space.