[en] We present the first search for galaxy counterparts of intervening high-z (2 < z < 3.6) sub-damped Lyα absorbers (sub-DLAs) and DLAs towards gamma-ray bursts (GRBs). Our final sample comprises five intervening sub-DLAs and DLAs in four GRB fields. To identify candidate galaxy counterparts of the absorbers we used deep optical- and near-infrared imaging, and low-, mid- and high-resolution spectroscopy acquired with 6-m to 10-m class telescopes, the Hubble and the Spitzer Space Telescopes. Furthermore, we used the spectroscopic information and spectral-energy-distribution fitting techniques to study them in detail. Our main result is the detection and spectroscopic confirmation of the galaxy counterpart of the intervening DLA at z = 3.096 in the field of GRB 070721B (zGRB = 3.6298) as proposed by other authors. We also identify good candidates for the galaxy counterparts of the two strong Mg ii absorbers at z = 0.6915 and 1.4288 towards GRB 050820A (zGRB = 2.615). The properties of the detected DLA galaxy are typical for Lyman-break galaxies (LBGs) at similar redshifts; a young, highly star-forming galaxy that shows evidence for a galactic outflow. This supports thehypothesis that a DLA can be the gaseous halo of an LBG. In addition, we report a redshift coincidence of different objects associated with metal lines in the same field, separated by 130–161 kpc. The high detection rate of three correlated structures on a length scale as short as ~150 kpc in two pairs of lines of sight is intriguing. The absorbers in each of these are most likely not part of the same gravitationally bound structure. They more likely represent groups of galaxies.