An analysis of the entropy dependence of the diffusion coefficient is presented in terms of the positional correlations in a fluid of hard spheres, with the objective to investigate the scaling law relating the diffusion coefficient and the excess entropy proposed many years ago and established empirically by the simulations. It is found that the exponential behavior between the reduced diffusion coefficient and the excess entropy is observable over a restricted range of densities, where the hydrodynamic behavior of the hard-sphere fluid is readily describable by a nearly exponential velocity autocorrelation function as prescribed by the Enskog theory. From this analysis, a semiempirical expression for the diffusion coefficient of the dense fluids is proposed in terms of the pair correlation function.