A statistical mechanical study of preferential solvation in supercritical fluids is presented. The study is focused on attractive mixtures, which are characterized by local density and composition enhancement in the vicinity of the solute molecule. The solute-solvent radial distribution functions are obtained from two versions of the integral equation formalism, both of which are designed for treating inhomogeneous systems. Model calculations are performed for a ternary Lennard-Jones mixture composed of a dilute solute and two solvent species, which are identical except for their interaction strength with the solute. It is shown that theoretical results agree well with Monte Carlo simulations in reproducing local solvent density and composition augmentation induced by the solute.