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Binaural noise-reduction algorithms based on multi-channel Wiener filter (MWF) are promising techniques to be used in binaural assistive listening devices. The real-time implementation of the existing binaural MWF methods, however, involves challenges to increase the amount of noise reduction without imposing speech distortion, and at the same time preserving the binaural cues of both speech and noise components. Although significant efforts have been made in the literature, most developed methods so far have focused only on either the former or latter problem. This paper proposes an alternative binaural MWF algorithm that incorporates the non-stationarity of the signal components into the framework. The main objective is to design an algorithm that would be able to select the sources that are present in the environment. To achieve this, a modified speech presence probability (SPP) and a single-channel speech enhancement algorithm are utilized in the formulation. The resulting optimal filter also avoids the poor estimation of the second-order clean speech statistics, which is normally done by simple subtraction. Theoretical analysis and performance evaluation using realistic recorded data shows the advantage of the proposed method over the reference MWF solution in terms of the binaural cues preservation, as well as the noise reduction and speech distortion.