We present a theoretical formulation for the solvent force constant and the asymmetry parameter which characterize the free energy profile governing the electrical potential fluctuations of the solvent molecules around solutes. This formulation allows us to calculate these parameters via the extended reference interaction site method (ex-RISM), an integral equation theory developed for molecular liquids and solutions. Since ex-RISM is inherently a non-linear theory, we can shed some light on the possible non-linear effects in the electrical potential fluctuations. The non-linear effects in the solvent force constants and the validity of the linear approximation will be examined based on the calculated results. The origin of the solute-dependent solvent force constants is briefly discussed.