The applicability of algebraic large eddy simulation (LES) closures of flame surface density (FSD) for head-on quenching of premixed turbulent flames by an isothermal inert wall has been assessed using 3D direct numerical simulations (DNS) data for different values of root-mean-square turbulent velocity fluctuation, Damkohler and Karlovitz numbers. An algebraic FSD closure, which has been reported to perform relatively satisfactorily among several available models, has been considered for this analysis alongside a model, which has recently been used for LES of flame-wall interaction. The applicability of previously proposed near-wall damping factors for flame surface wrinkling and consumption rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations has also been assessed for LES based on the current a-priori DNS analysis. It has been found that existing models considered for this analysis do not predict the near-wall behavior of the FSD accurately for all cases considered here. Furthermore, the widely used expression has been found to overpredict the combined reaction rate and molecular diffusion term in the near-wall region but the agreement between these terms gets better away from the wall. However, does not sufficiently capture the local behavior of the density-weighted surface filtered displacement speed so the correlation coefficient between and the combined reaction rate and molecular diffusion term remains much smaller than unity. It has been found that the damping factors proposed for RANS are not suitable for LES, and they severely damp the near-wall magnitudes of FSD and the combined reaction rate and molecular diffusion term and lead to significant under-predictions. Based on this a-priori analyses new near-wall modifications to the generalized FSD and the combined reaction and molecular diffusion term have been proposed in the context of LES, which have been found to capture both qualitative and quantitative trends obtained from DNS data.