Nucl.Phys.A 1047(2024)122876 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.