The study of collective excitations in quantum fluids is fundamental to understand nonequilibrium dynamics and many-body interactions. In this work, we report the first experimental measurement of correlations between collective excitation modes—Bogoliubov modes—in a quantum fluid of microcavity exciton-polaritons. By using a balanced detection set-up, we measure intensity correlation between the normal and ghost branches, probing the fluctuation dynamics of polariton fluids and extracting the spectral correlations of Bogoliubov excitations. We observe a clear enhancement of the intensity correlations when the polariton fluid operates near the turning point of the bistabilty due to the emergence of correlated phonon-like excitations. These correlations, seeded by quantum and thermal fluctuations, provide insights into the role of the nonlinear and phononic interactions in the collective excitations of a polariton quantum fluid.