Monitoring chlorine concentrations (CCs) plays an essential role in water quality management of water distribution networks (WDNs). However, placing water quality sensors at every junction is infeasible due to their high costs. Consequently, sensors are typically placed at a subset of junctions, which challenges the pursuit of a comprehensive assessment of chlorine concentrations throughout the network, which is necessary to ensure a safe water supply to end users. In this study, we tackle this challenge by introducing a framework for water quality state estimation (WQSE) using Graph Neural Networks (GNNs). WQSE reconstructs unmeasured CCs throughout the network based on measurements from a limited number of sensors distributed across the WDN. This study developed two GNN models to estimate CCs at all junctions. In the first model, a GNN model is trained to conduct Static Prediction (SP) of CCs based on data collected from a specific sensor network design (i.e., sensor placement configuration). In the second model, a GNN model is trained using data from various sensor designs to produce a generalized GNN model capable of conducting Dynamic Prediction (DP) of CCs. That is, the model can reconstruct CCs throughout the WDN based on data collected from any sensor network, even if different from those it was trained. The two models were applied to the C-Town benchmark network, considering that only 3% of the junctions were equipped with sensors. The results of the two models highlighted their ability to produce accurate predictions for intermediate junctions while struggling to predict CCs at dead-end junctions. The SP model outperformed the DP model in terms of accuracy. In addition, the SP model was shown to be robust against noisy measurements and produced better predictions than the physical model. The DP model stood out for its flexibility in being applicable to different sensor network designs. Furthermore, the DP model accuracy was shown to be highly dependent on the input sensor design, allowing for its implementation in sensor placement optimization.