In large eddy simulation of turbulent flow, because of the spatial filter, inhomogeneity and anisotropy affect the subgrid stress via the mean flow gradient. A method of evaluating the mean effects is to split the subgrid stress tensor into “rapid” and “slow” parts. This decomposition was introduced by Shao et al. (1999) and applied to A Priori tests of existing subgrid models in the case of a turbulent mixing layer. In the present work, the decomposition is extended to the case of a passive scalar in inhomogeneous turbulence. The contributions of rapid and slow subgrid scalar flux, both in the equations of scalar variance and scalar flux, are analyzed. A Priori numerical tests are performed in a turbulent Couette flow with a mean scalar gradient. Results are then used to evaluate the performances of different popular subgrid scalar models. It is shown that existing models can not well simulate the slow part and need to be improved. In order to improve the modeling, an extension of the model proposed by Cui et al. (2004) is introduced for the slow part, whereas the Scale-Similarity model is used reproduce the rapid part. Combining both models, A Priori tests lead to a better performance. However, the remaining problem is that none eddy-diffusion model can correctly represent the strong scalar dissipation near the wall. This problem will be addressed in future work.