The effects of pressure on the physical behavior of sub-grid scalar fluxes and their modeling have been analyzed based on a-priori analysis of a Direct Numerical Simulation database of turbulent premixed Bunsen flames featuring different pressure levels. Due to an increasing ratio of the hydrodynamic to critical length scale for the occurrence of Darrieus-Landau instability, the flames become increasingly hydrodynamically unstable with increasing pressure. An increasing extent of counter-gradient transport with increasing pressure has been found, consistent with recent observations reported in the existing literature. The performance of a selection of well-known Large Eddy Simulation models for sub-grid turbulent scalar flux from literature has been assessed for a range of filter widths for different thermodynamic pressures. While some models show high correlations with the sub-grid scalar flux extracted from explicitly filtered Direct Numerical Simulation data, and a reasonable quantitative prediction of the sub-grid turbulent scalar flux magnitude for small values of filter width to flame thickness ratio, several models considerably underpredict the sub-grid scalar flux magnitudes for large filter widths. This effect becomes more pronounced for higher pressures as the length scale separation between the filter width and flame thickness increases with increasing pressure.