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 textit{Swift}/BAT sample in order to identify nearby ($d_Llesssim 200$ 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 a NS radio flare at a distance of $sim 100$ Mpc. However, an origin related to a persistent radio source unrelated to the GRB cannot be excluded given the high chance of false positives in error regions as large as those considered here. Further radio follow-up observations are needed to better understand the origin of this source.
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