  We study $\eta$ photoproduction off the deuteron ($\gamma d\to\eta pn$) at a
special kinematics: $\sim 0.94$ GeV of the photon beam energy and $\sim
0^\circ$ of the scattering angle of the proton. This kinematics is ideal to
extract the low-energy $\eta$-nucleon scattering parameters such as $a_{\eta
N}$ (scattering length) and $r_{\eta N}$ (effective range) because the
$\eta$-nucleon elastic scattering is significantly enhanced. We show that if a
ratio $R$, the $\gamma d\to\eta pn$ cross section divided by the $\gamma
p\to\eta p$ cross section convoluted with the proton momentum distribution in
the deuteron, is measured with 5% error, ${\rm Re}[a_{\eta N}]$ (${\rm
Re}[r_{\eta N}]$) can be determined at the precision of $\sim\pm$0.1 fm
($\sim\pm$0.5 fm), significantly narrowing down the currently estimated range
of the parameters. The measurement is ongoing at the Research Center for
Electron Photon Science (ELPH), Tohoku University.
