We propose a novel Power Spectral Density (PSD) estimator for multi-microphone systems operating in reverberant and noisy conditions. The estimator is derived using the maximum likelihood approach and is based on a blocked and pre-whitened additive signal model. The intended application of the estimator is in speech enhancement algorithms, such as the Multi-channel Wiener Filter (MWF) and the Minimum Variance Distortionless Response (MVDR) beamformer. We evaluate these two algorithms in a speech dereverberation task and compare the performance obtained using the proposed and a competing PSD estimator. Instrumental performance measures indicate an advantage of the proposed estimator over the competing one. In a speech intelligibility test all algorithms significantly improved the word intelligibility score. While the results suggest a minor advantage of using the proposed PSD estimator, the difference between algorithms was found to be statistically significant only in some of the experimental conditions.