In today's digital age, coverage prediction is essential for optimizing wireless networks and improving user experience. While numerous path loss models and advanced machine learning algorithms have been developed to achieve high prediction performance, they predominantly operate within a centralized learning paradigm. While effective, this conventional approach often suffers from scalability and privacy limitations that are critical to the successful deployment of wireless maps. Conversely, in this paper, we propose a novel decentralized approach based on a federated learning long short-term memory (LSTM) model to accurately predict network coverage in indoor environments. The proposed FedLSTM is a method that allows multiple users, or clients, to train the model without sharing their personal data directly with a central server. In an experimental setup, we used real data collected from numerous clients moving along different paths. The FedLSTM model is evaluated in terms of root mean square error (RMSE), mean absolute error (MAE), and R2. Furthermore, compared to a centralized counterpart, FedLSTM shows a slight increase in RMSE from 2.4 dBm to 2.5 dBm and an increase in MAE from 1.7 dBm to 1.9 dBm. In addition, we evaluate the proposed FedLSTM considering variations in the number of participating clients and the number of local training epochs. The results show that even devices with limited computational power can meaningfully contribute to the training of the federated model, with fewer epochs achieving competitive results. Graphical analyses of the radio environment maps (REMs) generated by both FedLSTM and the centralized LSTM highlight their similarities. However, FedLSTM provides client privacy while reducing communication overhead and server strain.INDEX TERMS Radio environment map (REM), coverage prediction, received signal strength indicator (RSSI), LiDAR sensor, federated learning.