Microphone arrays usually combine multiple input signals into one output signal, such that spatial information on the sound sources is not included in the output signal. Since spatial information on the sound sources may increase the intelligibility of a speech signal that is perceived by a human listener, recent works aim to include this spatial information in the output of the microphone array by utilizing binaural cues preservation. More current works apply binaural sound reproduction (BSR) using spherical microphone arrays by incorporating the head related transfer functions (HRTFs) in the weight function of a conventional maximum-directivity beamformer. However, the HRTFs may affect the optimality of beamformers that were already designed to provide a maximal directivity without the HRTFs. This work presents a more general mathematical framework than previously presented for the incorporation of HRTFs in the weight function, which allows the optimization of the weight function using an averaged maximum-directivity criterion under the condition that the HRTFs are already incorporated. It is shown that the proposed optimized BSR beamformer achieves higher directivity index.