  The multi-messenger observation of gamma-ray burst (GRB)\,170817A from the
nearby binary neutron-star merger GW170817 demonstrated that low-energy
$\gamma$-ray emission can be observed at relatively large angles from GRB jet
axes. If such structured emission is typical, then the currently known sample
of short GRBs with no distance measurements may contain multiple nearby
off-axis events whose delayed afterglows could have gone undetected. These
nearby neutron star mergers may produce telltale radio flares peaking years
after the prompt GRB emission that could still be observable. Here, we show
that several short GRBs observed by the Burst Alert Telescope (BAT) on the Neil
Gehrels \textit{Swift} satellite, with no identified afterglow and no distance
measurement, could potentially be associated with radio flares detectable by
sensitive cm-wavelength radio facilities such as the Karl G. Jansky Very Large
Array. We also examine optical follow-up observations that have been carried
out for these events, and find that a nearby GW170817-like kilonova is ruled
out for only a third of them.
