By means of an effective potential associated with a constrained equilibrium measure and apt to study frozen systems, we investigate glassy freezing in simple liquids in the hypernetted chain (HNC) approximation. Unlike other classical approximations of liquid theory, freezing is naturally embedded in the HNC approximation. We give a detailed description of the freezing transition that is analogous to the one given in a large class of mean-field long range spin glass. We compare our findings with Monte Carlo simulations of the same system and conclude that many of the qualitative features of the transition are captured by the approximated theory.