An estimate of the power spectral density (PSD) of the late reverberation is often required by dereverberation algorithms. In this work, we derive a novel multichannel maximum likelihood (ML) estimator for the PSD of the reverberation that can be applied in noisy environments. Since the anechoic speech PSD is usually unknown in advance, it is estimated as well. As a closed-form solution for the maximum likelihood estimator is unavailable, a Newton method for maximizing the ML criterion is derived. Experimental results show that the proposed estimator provides an accurate estimate of the PSD, and outperforms competing estimators. Moreover, when used in a multi-microphone dereverberation and noise reduction algorithm, the best performance in terms of the log-spectral distance is achieved when employing the proposed PSD estimator.