Wireless acoustic sensor network (WASN) has a wide range of applications in internet of things, where signal estimation is one of the network design objectives. Due to the existence of ambient noises, the recorded audio signals are inevitably corrupted, resulting in a low signal-to-noise ratio (SNR), which triggers the necessity of signal enhancement. As using all sensor measurements brings a large amount of data transmissions and computational cost, the narrowband sensor selection was proposed to choose an informative subset of sensors to perform noise reduction in the audio context. However, the resulting frequency-dependent selection status has to be switched across frequencies. In order to avoid the complicated switching operations, we consider frequency-invariant sensor selection in this work. We propose to minimize the total power consumption over the WASN by constraining the broadband SNR, which can be solved using broadband semi-definite optimization (BroadOpt) or narrowband voting (NaVo) approaches. In order to further reduce the time complexity, we propose two near-optimal greedy methods, including gradient removal (GradR) and weighted input SNR removal (SnrR). As comparison, we also show a broadband energy removal (EnergyR) method. The greedy methods remove one sensor at each iteration from the complete network until the performance constraint is not satisfied. Numerical results using a simulated large-scale WASN show that the greedy methods can achieve a comparable performance compared to the optimization based counterparts, while the corresponding time complexity is much lower. In general, the sensors around the target source and the fusion center are more likely to be selected.