Allostery describes altered protein function at one site due to a perturbation at another site. One mechanism of allostery involves correlated motions, which can occur even in the absence of substantial conformational change. We present a novel method, "MutInf", to identify statistically significant correlated motions from equilibrium molecular dynamics simulations. Our approach analyzes both backbone and sidechain motions using internal coordinates to account for the gear-like twists that can take place even in the absence of the large conformational changes typical of traditional allosteric proteins. We quantify correlated motions using a mutual information metric, which we extend to incorporate data from multiple short simulations and to filter out correlations that are not statistically significant. Applying our approach to uncover mechanisms of cooperative small molecule binding in human interleukin-2, we identify clusters of correlated residues from 50 ns of molecular dynamics simulations. Interestingly, two of the clusters with the strongest correlations highlight known cooperative small-molecule binding sites and show substantial correlations between these sites. These cooperative binding sites on interleukin-2 are correlated not only through the hydrophobic core of the protein but also through a dynamic polar network of hydrogen bonding and electrostatic interactions. Since this approach identifies correlated conformations in an unbiased, statistically robust manner, it should be a useful tool for finding novel or "orphan" allosteric sites in proteins of biological and therapeutic importance.