The capture and reproduction of spatial audio is becoming increasingly popular, with the mushrooming of applications in teleconferencing, entertainment and virtual reality. Two popular methods include high order Ambisonics and beamforming-based binaural reproduction, which are mainly studied with spherical arrays. However, a design framework for arrays with a less regular configuration has yet to be formulated and studied. This paper studies a method for binaural reproduction with general arrays, based on the direct estimation of the binaural signal from the array measurements. A simulation study shows that this method is capable of performing binaural reproduction with high accuracy over a limited frequency range, even with a small six-microphone array.