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 the calculation of these parameters via the extended reference interaction site method, an integral equation theory developed for molecular liquids and solutions. Since the method is inherently a nonlinear theory, we can shed some light on the possible nonlinear effects in the electrical potential fluctuations. The nonlinear effects in the solvent force constant and the validity of the linear approximation will be examined by a series of calculations for monatomic and diatomic solutes immersed in a simple dipolar solvent. The origin of the solute-dependent solvent force constant is discussed.