In distributed acoustic sensor networks, only a few nodes make a significant contribution to speech enhancement tasks. Using these most informative nodes instead of the entire network not only avoids unnecessary energy consumption but also prolongs the lifetime of sensors. To this end, a sensor selection method for distributed speech enhancement is proposed. The best subset of microphone nodes is determined by maximizing the signal-to-noise ratio (SNR), while keeping the activated nodes connected with each other. The above criterion involves an integer and non-linear programming, which is linearized with multiple base-3 sub-optimization problems, and each of them is solved by a state-of-the-art steepest descent (SD) algorithm. In addition, a greedy searching strategy is presented to select sensors rapidly. Finally, a distributed SD algorithm is further derived, which is more suitable for distributed sensor networks. The proposed method can obtain the optimal subnetwork in noisy and reverberant environments. Unlike the existing approaches, it can select nodes from a microphone network with arbitrary communication graphs. Moreover, it requires only local communications among nodes without an external central processor. Experimental results confirm the validity of the proposed method.