Beamforming techniques are popular in speech-related applications due to their effective spatial filtering capabilities. Nonetheless, conventional beamforming techniques generally depend heavily on either the target's direction-of-arrival (DOA), relative transfer function (RTF) or covariance matrix. This paper 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 speech signal parameters mentioned earlier. The IANS framework combines a null-steering beamformer (NSBF) to generate a set of beamformed outputs, and STOI-Net, to determine the optimal result. Experimental results indicate that IANS can produce intelligibility-enhanced signals using a small dual-microphone array. The results are comparable to those obtained by null-steering beamformers with given knowledge of DOAs.