We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. In particular, we exploit the increasing correlation between the exchanged values throughout the iterations of the consensus algorithm in order to design an efficient progressive quantization scheme. We implement a fixed-resolution uniform quantizer in each sensor, where refined quantization is achieved by reducing the quantization intervals with the convergence of the consensus algorithm. We propose a recurrence relation for computing the quantization parameters that depend on the network topology and the communication rate. We further propose a simple exponential model for the adaptation of the quantization intervals. Finally, simulation results demonstrate the effectiveness of the progressive quantization scheme that leads to the consensus solution even at low communication rate.