  We study the production of $X(3872)$ mesons in photon-induced nuclear
reactions near the threshold within the collision model based on the nuclear
spectral function. The model accounts for direct photon-nucleon $X(3872)$
production processes as well as five different scenarios for their internal
structure. We calculate the absolute and relative excitation functions for
$X(3872)$ production off $^{12}$C and $^{184}$W target nuclei at near-threshold
incident photon energies of 8--16 GeV, the absolute differential cross sections
for their production off these target nuclei at laboratory angles of
0$^{\circ}$--10$^{\circ}$ and for incident photon energy of 13 GeV as well as
the A dependences of the relative (transparency ratios) cross sections for
$X(3872)$ production from ${\gamma}A$ collisions at photon energies around 13
GeV within the adopted scenarios for the $X(3872)$ meson internal structure. We
show that the absolute and relative observables considered reveal distinct
sensitivity to these scenarios. Therefore, the measurement of such observables
in a dedicated experiment at the CEBAF facility in the near-threshold energy
range will allow us to get valuable information on the $X(3872)$ inner
structure.
