  A procedure is proposed which accounts for final state interaction
corrections for near threshold meson production in nucleon-nucleon scattering.
In analogy with the Watson-Migdal approximation, it is shown that in the limit
of extremely strong final state effects, the amplitude factorizes into a
primary production amplitude and an elastic scattering amplitude describing a
$3 \to 3$ transition. This amplitude determines the energy dependence of the
reaction cross section near the reaction threshold almost solely. The
approximation proposed satisfies the Fermi-Watson theorem and the coherence
formalism. Application of this procedure to meson production in nucleon-nucleon
scattering shows that, while corrections due to the meson-nucleon interaction
are small for s-wave pion production, they are crucial for reproducing the
energy dependence of the $\eta$ production cross section.
