We apply a spectral stacking technique to Westerbork Synthesis Radio Telescope observations to measure the neutral atomic hydrogen content (H I) of nearby galaxies in and around galaxy groups at z < 0.11. Our sample includes 577 optically selected galaxies (120 isolated galaxies and 457 satellites) covering stellar masses between 1010 and 1011.5 M☉, cross-matched with Yang’s group catalogue, with angular and redshift positions from the Sloan Digital Sky Survey. We find that the satellites in the centres of groups have lower H I masses at fixed stellar mass and morphology (characterized by the inverse concentration index) relative to those at larger radii. These trends persist for satellites in both high-mass (Mhalo > 1013.5 h-1 M☉) and low-mass (Mhalo ≤ 1013.5 h-1 M☉) groups, but disappear if we only consider group members in low local density (Σ < 5 gal Mpc-2) environments. Similar trends are found for the specific star formation rate. Interestingly, we find that the radial trends of decreasing H I mass with decreasing group-centric radius extend beyond the group virial radius, as isolated galaxies close to larger groups lack H I compared with those located more than ∼3.0 R180 away from the centre of their nearest group. We also measure these trends in the late-type subsample and obtain similar results. Our results suggest that the H I reservoir of galaxies can be affected before galaxies become group satellites, indicating the existence of pre-processing in the infalling isolated galaxies.