We study the effect of intracellular ion diffusion on ionic currents permeating through the cell membrane. Ion flux across the cell membrane is mediated by special proteins forming specific channels. The structure of potassium channels have been widely studied in recent years with remarkable results: very precise measurements of the true current across a single channel are now available. Nevertheless, a complete understanding of the behavior of the channel is still lacking, though molecular dynamics and kinetic models have provided partial insights. In this paper we demonstrate, by analyzing the KcsA current-voltage currents via a suitable lattice model, that intracellular diffusion plays a crucial role in the permeation phenomenon. The interplay between the selectivity filter behavior and the ion diffusion in the intracellular side allows a full explanation of the current-voltage curves.