Speech intelligibility prediction (SIP) models have been used as objective metrics to assess intelligibility for hearing-impaired (HI) listeners. In the Clarity Prediction Challenge 2 (CPC2), non-intrusive binaural SIP models based on transformers showed high prediction accuracy. However, the self-attention mechanism theoretically incurs high computational and memory costs, making it a bottleneck for low-latency, power-efficient devices. This may also degrade the temporal processing of binaural SIPs. Therefore, we propose Mamba-based SIP models instead of transformers for the temporal processing blocks. Experimental results show that our proposed SIP model achieves competitive performance compared to the baseline while maintaining a relatively small number of parameters. Our analysis suggests that the SIP model based on bidirectional Mamba effectively captures contextual and spatial speech information from binaural signals.