In addition to estimating the positions of acoustical sources, estimating their mutual correlations can yield important informations about the sources. A simple example is the pairing of a source and its images in a reverberant environment, as they are perfectly correlated. Jointly estimating the positions and correlations of sources is a computational challenge, both in memory and time complexity since the entire covariance matrix of the sources has to be recovered (and not only its diagonal as for standard powers estimation). Correlated sources are also known to prevent the application and subspace-based methods such as MUSIC. We propose to estimate the covariance matrix of the sources in a greedy way, using the Orthogonal Least Squares algorithm. This algorithm allows efficient identification of the sources, with reasonable computational requirements. The performances of the method are demonstrated with experimental measurements, using correlated sources (multiple sources emitting the same signal, or a unique source with a reflection).