The multi-messenger discovery of gravitational waves (GWs) and light from the binary neutron star (NS) merger GW170817, associated with gamma-ray burst (GRB) 170817A and kilonova AT2017gfo, has marked the start of a new era in astrophysics. GW170817 has confirmed that binary NS mergers are progenitors of at least some short GRBs. The peculiar properties of the GRB 170817A radio afterglow, characterized by a delayed onset related to the off-axis geometry, have also demonstrated how some nearby short GRBs may not be identified as such with standard short-timescale electromagnetic follow-up observations. Building upon this new information, we performed late-time radio observations of a sample of four short GRBs with unknown redshift and no previously detected afterglow in the Swift/BAT sample in order to identify nearby (d L Mpc) off-axis GRB candidates via their potential late-time radio signatures. We find a previously uncatalogued radio source within the error region of GRB 130626 with a 3-6, GHz flux density consistent with an NS radio flare at a distance of ∼100 Mpc. An origin related to a persistent radio source unrelated to the GRB cannot be excluded nor confirmed given the high chance of false positives in error regions as large as those considered here, and the limited time baseline of our observations. Further radio (and X-ray) follow-up observations are needed to better understand the origin of this source.