Do pulsar timing arrays observe merging primordial black holes?

In this letter we evaluate whether the gravitational wave background recently observed by a number of different pulsar timing arrays could be due to merging primordial supermassive black hole binaries. We find that for homogeneously distributed primordial black holes this possibility is inconsistent with the strong cosmological and astrophysical constraints on their total abundance. If the distribution exhibits some clustering, however, the merger rate will in general be enhanced, opening the window for a consistent interpretation of the PTA data in terms of merging primordial black holes.