Recently instantaneous normal mode analysis has revealed an interesting similarity of the solvent dynamical influence on two rather different phenomena, namely vibrational energy relaxation (VER) and nonpolar solvation dynamics (NPSD). In this work we show that this similarity can be rationalized from a mode coupling theoretic analysis of the dynamic response of a dense liquid. The present analysis demonstrates that VER and the initial NPSD are coupled primarily to the binary part of the frequency dependent frictional response of the liquid. It is found that for strong solute-solvent interaction, the initial decay of nonpolar solvation dynamics can proceed with time constant less than 100 fs. In addition, a very good agreement between the calculated and the simulated VER rates have been obtained for a large range of frequency.