In this paper, we consider source coding in wireless acoustic sensor networks (WASNs). A WASN is a network of sensors, where each sensor is equipped with a microphone and thereby forming a distributed microphone array. In addition to a microphone, the sensors communicate via radio channels. Thus, a sensor observes an acoustic noisy measurement in addition to receiving a coded correlated noisy measurement from a neighboring sensor node. Given a set of sensors, the problem is to efficiently encode the noisy observations and/or re-encode the received coded noisy observations. Furthermore, one seeks a routing strategy that e.g., minimizes the sum rate subject to some distortion constraints. Towards that end, we define a new source coding concept related to WASNs which we denote sequential remote source coding, and present an achievable rate region in the quadratic Gaussian case.