Molecular dynamics and Gibbs ensemble Monte Carlo simulations have been used to investigate solvation structures in a dilute supercritical solution of two particle types interacting via Lennard-Jones potentials, Spatial correlations evidenced in the solute-solvent radial distribution functions near the critical point are found to depend strongly on the simulation cell size, There are significant differences between the solvent-solvent and solute-solvent radial distribution functions in the liquid and supercritical states. The mechanism of the development of a dynamic solvation structure around the solute is revealed in the density fluctuations in the critical region. In the liquid state thermal motion prevents strong pair correlations from appearing, masking underlying differences in the solvent-solvent and solute-solvent interaction potentials.