A subgrid model for soot dynamics is developed for large-eddy simulation (LES). The model uses a Method of Moments approach with Lagrangian Interpolative Closure (MOMIC) so that no a priori knowledge of the particles distribution is required. The soot model is implemented within a subgrid mixing and combustion model so that the reaction-diffusion-MOMIC coupling is possible without requiring ad hoc filtering. A relatively detailed multi-species ethylene-air kinetics is employed for the gas phase combustion, and is used here to study the effect of employing a detailed species variable diffusion coefficients on soot production in turbulent premixed flames. The results show that the variable transport properties affect the general structure of the flame in the form of wider curvature probability density function tails and higher turbulent flame speed. In addition, the effect on the relative thermal to molecular diffusivity in the subgrid level (Lewis number effect) changes the surface growth rate and the soot production level.