In this talk we apply the photoproduction framework recently implemented into the Pythia 8 Monte Carlo event generator to study the potential of photo-nuclear dijets in ultra-peripheral Pb+Pb collisions at the LHC to further constrain the nuclear PDFs. These events can be described as $\gamma$A collisions where the relevant part of the flux of quasi-real photons from heavy-ions is obtained by using the equivalent photon approximation and cutting out impact-parameter values which would lead to hadronic interactions between the beam particles. In particular, we quantify the small-$x$ reach with different jet kinematics and show how well the values of $x$ derived from reconstructed jet momenta are correlated with the actual values of partonic momentum fractions probed in these measurements. Also the contributions from direct and resolved photons are separately presented. To demonstrate the potential, we compare the expected experimental uncertainties to the current nuclear-PDF errors and discuss other theoretical uncertainties including the uncertainty arising from poorly-constrained photon PDFs. We find that such a measurement would potentially provide a considerable reduction of the nuclear PDF uncertainties in a region $10^{-4} \lesssim x \lesssim 10^{-2}$.