  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
($d_L\lesssim 200$ 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.
