The target speech extraction has attracted widespread attention in recent years. In this work, we focus on investigating the dynamic interaction between different mixtures and the target speaker to exploit the discriminative target speaker clues. We propose a special attention mechanism without introducing any additional parameters in a scaling adaptation layer to better adapt the network towards extracting the target speech. Furthermore, by introducing a mixture embedding matrix pooling method, our proposed attention-based scaling adaptation (ASA) can exploit the target speaker clues in a more efficient way. Experimental results on the spatialized reverberant WSJ0 2-mix dataset demonstrate that the proposed method can improve the performance of the target speech extraction effectively. Furthermore, we find that under the same network configurations, the ASA in a single-channel condition can achieve competitive performance gains as that achieved from two-channel mixtures with inter-microphone phase difference (IPD) features.