Beamforming techniques are popular in speech-related applications because of their effective spatial filtering capabilities. Nonetheless, conventional beamforming techniques generally depend on the target’s direction-of-arrival (DOA), relative transfer function (RTF), or covariance matrix. This study presents a new approach, the intelligibility-aware null-steering (IANS) beamforming framework, which uses the STOI-Net intelligibility prediction model to improve speech intelligibility without prior knowledge of the aforementioned speech signal parameters. The IANS framework combines a null-steering beamformer (NSBF) to generate a set of beamformed outputs, and STOI-Net, to determine the optimal result. The experimental results indicate that the IANS framework can produce intelligibility-enhanced signals using a small dual-microphone array. The results are comparable to those obtained by null-steering beamformers with a given knowledge of the DOAs.