Fast Radio Bursts (FRBs) have so far been detected serendipitously across the sky. We consider the possible enhancement in the FRB rate in the direction of galaxy clusters, and compare the predicted rate from a large sample of galaxy clusters to the expected cosmological mean rate. We show that clusters offer better prospects for a blind survey if the faint end of the FRB luminosity function is steep. We find that for a telescope with a beam of ~1 deg^2, the best targets would be either nearby clusters such as Virgo or clusters at intermediate cosmological distances of few hundred Mpc, which offer maximal number of galaxies per beam. We identify several galaxy clusters which have a significant excess FRB yield compared to the cosmic mean. The two most promising candidates are the Virgo cluster containing 1598 galaxies and located 16.5 Mpc away and S34 cluster which contains 3175 galaxies and is located at a distance of 486 Mpc.