We consider the problem of a single parameter estimation by a sensor network with a fusion center (FC). Sensor observations are corrupted by additive noises which can have arbitrary spatial correlation. Due to a bandwidth constraint each sensor is only able to transmit a finite number of bits. The fusion center combines messages from the sensors to produce a parameter estimator, which is required to have Mean Square Error (MSE) within a constant factor of that of the Best Linear Unbiased Estimator (BLUE). We show that total sensor transmitted power can be minimized while meeting target MSE requirement if quantization levels are determined jointly by the fusion center using the knowledge of noise covariance matrix. By numerical examples we show that energy saving up to 70% can be achieved when compared to uniform quantization strategy when each sensor generates the same number of bits.