  The $\omega$-meson photoproduction, $\gamma+p\to p+\omega$, is studied in the
framework of a model, containing $\pi$-meson exchange in t-channel and
nucleon-exchange in s- and u-channels. Considering both $\omega NN$-coupling
constants in the region of time-like meson four momenta as the free parameters,
we find different sets of solutions for these constants from the existing data
on the t-dependence of the differential cross sections, $d\sigma(\gamma+p\to
p+\omega)/dt$, in the near threshold region $E_{\gamma}\leq 2$ GeV. These sets
of $\omega NN$-coupling constants, corresponding to destructive and
constructive $\pi\bigotimes N$-interference contributions to $d\sigma/dt$ can
be well distinguished by measurements of beam asymmetry, induced by linear
photon polarization.
