We propose that the best sites to search for soft gamma repeaters (SGRs) outside the Local Group are galaxies with active massive-star formation. Different possibilities to observe SGR activity from these sites are discussed. In particular, we have searched for giant flares from the nearby galaxies (∼2-4 Mpc away) M82, M83, NGC 253 and 4945 in the Burst and Transient Source Experiment (BATSE) data. No candidate giant SGR flares were found. The absence of such detections implies that the rate of giant flares with energy release in the initial spike above 0.5x1044 erg is less than 1/30/yr in our Galaxy. However, hyperflares similar to that of 2004 December 27 can be observed from larger distances. Nevertheless, we do not see any significant excess of short GRBs from the Virgo galaxy cluster or from the galaxies Arp 299 and NGC 3256 (both with extremely high star formation rates). This implies that the Galactic rate of hyperflares with energy release ∼1046 erg is less than ∼10–3/yr. With this constraint the fraction of possible extragalactic SGR hyperflares among BATSE's short GRBs should not exceed a few per cent. We present the list of short GRBs coincident with the galaxies mentioned above, and discuss the possibility that some of them are SGR giant flares. We propose that the best target for the observations of extragalactic SGR flares with Swift is the Virgo cluster.