  Off-shell propagation of nucleons is neglected in one-body transport models
of heavy-ion collisions, but it could be significant in processes that are
limited by phase space, such as the threshold production of heavy particles. We
estimate the relative magnitude of off-shell production to on-shell production
of the N$^*$(1535) resonance in heavy ion collisions. In the region where the
on-shell production is dominated by a~two-step mechanism with an intermediate
$\Delta$, we find that the contribution of off-shell scattering between
projectile and target nucleons is indeed small. Beyond the latter contribution,
however, correlations in the initial wave function produce off-shell
contributions which can exceed those of the on-shell $\Delta$ mechanism.
