Noise reduction is a fundamental step in signal processing in binaural hearing aids. In general, this procedure is characterized by an optimization algorithm that minimizes a cost function composed of a combination of the Wiener multichannel filter and constraints or penalty terms that aim to guarantee the preservation of binaural spatial information. However, the cost function is non-convex, which makes its solution demand a high computational cost. In this work we propose a computationally efficient approach for noise reduction with preservation of binaural spatial information, based on a convex relaxation of the original optimization problem. Experiments indicate that the proposed technique achieves performance comparable to state-of-the-art algorithms in terms of noise reduction and preservation of the perception of the spatial location of point sources, but with an extremely reduced processing time.