Simulation studies of the atomic shear stress in the local potential energy minima (inherent structures) are reported for binary liquid mixtures in 2D and 3D. These inherent structure stresses are fundamental to slow stress relaxation and high viscosity in supercooled liquids.We find that the atomic shear stress in the inherent structures (IS) of both liquids at rest exhibits slowly decaying anisotropic correlations. We show that the stress correlations contributes significantly to the variance of the total shear stress of the IS configurations and consider the origins of the anisotropy and spatial extent of the stress correlations.