A discrete lattice model is developed to describe diffusion-mediated polymerization occurring within mesopores, where reaction is enhanced at catalytic sites distributed within the interior of the pores. Diffusive transport of monomers and polymers is one-dimensional, diffusion coefficients for the latter decreasing with polymer length. Kinetic Monte Carlo simulation is utilized to analyze model behavior focusing on a "clogging" regime, where the amount of polymer within the pores grows. We characterize the evolution of the overall and mean length of polymers, the mean number of polymers, as well as the polymer spatial and length distributions.