We present an analysis of the second epoch HST WFC3 F110W near-Infrared (NIR) imaging data of the globular cluster M4. The new dataset suggests that one of the previously suggested four brown dwarf candidates in this cluster is indeed a high-probability cluster member. The position of this object in the NIR colour magnitude diagrams (CMDs) is in the white dwarf/brown dwarf area. The source is too faint to be a low-mass main sequence star, but, according to theoretical considerations, also most likely somewhat too bright to be a bona-fide brown dwarf. Since we know that the source is a cluster member, we determined a new optical magnitude estimate at the position the source should have in the optical image. This new estimate places the source closer to the white dwarf sequence in the optical-NIR CMD and suggests that it might be a very cool (T_eff < 4500 K) white dwarf at the bottom of the white dwarf cooling sequence in M4, or a white dwarf/brown dwarf binary. We cannot entirely exclude the possibility that the source is a very massive, bright brown dwarf, or a very low-mass main sequence star, however, we conclude that we still have not convincingly detected a brown dwarf in a globular cluster, but we expect to be very close to the start of the brown dwarf cooling sequence in this cluster. We also note that the main sequence ends at F110W approx.22.5 mag in the proper-motion cleaned CMDs, where completeness is still high.