In this work, taking the perspective of Mobile Virtual Network Operators (MVNOs), we tackle the multi-slice traffic forecasting problem, while respecting the data privacy of users. To this end, we propose the Federated Proximal Long Short-Term Memory (FPLSTM) framework, which allows MVNOs to train at each base station their local models with their private datasets, without compromising data privacy. Prediction results obtained by evaluating the models on a real-world dataset indicate that the forecast of FPLSTM is as accurate as state-of-the-art solutions while ensuring data privacy as well as computation and communication costs efficiency.