ABSTRACT 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 superluminous 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 ∼20 h 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 × 10−6. 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.