We present VLT (FORS1) photometry of the lower main sequence (MS) of the Galactic Globular Cluster (GGC) NGC 6397, for stars located in 2 fields extending from a region near the cluster center out to ~ 10. The obtained CMD shows a narrow MS extending down to V ~ 27 (figure c), much deeper than any previous ground based study and comparable with previous HST photometry (Cool et al. 1996). The comparison between observed MS Luminosity Functions (LFs) derived for 2 annuli at different radial distance from the center of the cluster shows a clear-cut correlation between their slope before reaching the turn-over, and the radial position of the observed fields inside the cluster area: the LFs become flatter with decreasing radius, a trend that is consistent with the interpretation of NGC 6397 as a dynamically relaxed system.