This work presents a noise reduction method with perceptually relevant preservation of the interaural time difference (ITD) of the residual noise in binaural hearing aids. The interaural coherence (IC) concept, previously applied to the Multichannel Wiener Filter (MWF) for preservation of the spatial subjective sensation of diffuse noise fields, is proposed here to both preserve and emphasize the ITD binaural cues of a directional acoustic noise source. It is demonstrated that the previously developed MWF-ITD technique may decrease the original IC magnitude of the processed noise, consequently increasing the variance of the interaural phase difference (IPD) of the output signals. It is shown that the MWF-IC technique concomitantly minimizes a nonlinear function of the difference between input and output IPD, which is strictly related to ITD, and preserves the natural coherence of the directional noise captured by the reference microphones. Objective measures and psychoacoustic experiments corroborate the theoretical findings, showing the MWF-IC technique provides relevant noise reduction, while preserving the original ITD subjective perception and original lateralization for a directional noise source. These results are especially relevant for hearing aid designers, since they indicate the MWF-IC as a noise reduction technique that provides resid-ual noise spatial preservation for both diffuse and directional noise sources in frequencies below 1.5 kHz.