  We investigate the possibility that the process of $\rho^{0}$-meson
photoproduction on proton, $\gamma+p\to p+\rho^{0}$, in the near threshold
region $E_{\gamma}< 2$ GeV, can be considered in the framework of model with
$\pi$-, $\sigma$- and N-exchanges. This suggestion is based on a study of the
t-dependence of differential cross section, $d\sigma(\gamma p \to p
\rho^{0})/dt$, which has been measured by SAPHIR Collaboration. We find that
the suggested model provides a good description of the experimental data with
new values of $\rho NN$-coupling constants in the region of the time-like
$\rho^{0}$-meson momentum. Our results suggest that such model can be
considered as a suitable nonresonant background mechanism for the future
discussion of possible role of nucleon resonance contributions. Our predictions
for $\rho^{0}$-meson photoproduction on neutron target and for beam asymmetry
on both proton and neutron targets are presented.
