  The analogy of the host galaxy of the repeating fast radio burst (FRB) source
FRB 121102 and those of long gamma-ray bursts (GRBs) and super-luminous
supernovae (SLSNe) has led to the suggestion that young magnetars born in GRBs
and SLSNe could be the central engine of repeating FRBs. We test such a
hypothesis by performing dedicated observations of the remnants of six GRBs
with evidence of having a magnetar central engine using the Arecibo telescope
and the Robert C. Byrd Green Bank Telescope (GBT). A total of $\sim 20$ hrs of
observations of these sources did not detect any FRB from these remnants. Under
the assumptions that all these GRBs left behind a long-lived magnetar and that
the bursting rate of FRB 121102 is typical for a magnetar FRB engine, we
estimate a non-detection probability of $8.9\times10^{-6}$. Even though these
non-detections cannot exclude the young magnetar model of FRBs, we place
constraints on the burst rate and luminosity function of FRBs from these GRB
targets.
