The recently discovered young supernova remnant (SNR) RX J0852.0-4622 has attracted much interest since its discovery because of the possibility that it may have been generated by the nearest supernova in recent history. We note the presence of two Parkes Multibeam Survey pulsars within the boundary of the remnant. We discuss the properties of the two pulsars and the likelihood of either of them being physically linked to the SNR. We tentatively suggest that, given the current uncertainties in the distance to RX J0852.0-4622, one of these pulsars, the 65-ms period PSR J0855-4644 could indeed be the compact remnant of this supernova explosion. If the pulsar birth site is at the geometrical centre of the nebula, then, for the transverse pulsar velocity to be reasonable, the SNR must be nearby (around 250 pc) and no younger than about 3000 yr old.