Free energy of contact ion-pair (CIP) formation of lithium ion with BF4- and PF6- in water, propylene carbonate (PC), dimethyl carbonate (DMC) are quantitatively analyzed using MD simulations combined with the energy representation method. The relative stabilities of the mono-, bi-, and tridentate coordination structures are assessed with and without solvent, and water, PC, and DMC are found to favor the CIP-solvent contact. The monodentate structure is typically most stable in these solvents, whereas the configuration is multidentate in vacuum. The free energy of CIP formation is not simply governed by the solvent dielectric constant, and microscopic analyses of solute-solvent interaction at a molecular level are then performed from energetic and structural viewpoints. Vacant sites of Li+ cation in CIP are solvated with three carbonyl oxygen atoms of PC and DMC solvent molecules, and the solvation is stronger for the monodentate CIP than for the multidentate. Energetically favorable solute-solvent configurations are shown to be spatially more restricted for the multidentate CIP, leading to the observation that the solvent favors the monodentate coordination structure.