Magnetic Resonance Imaging (MRI) is a crucial medical imaging technique for diagnosing various health conditions. However, the reconstruction of high-quality MRI images is computationally intensive and often requires extensive data sharing, posing challenges in terms of privacy and security. Federated learning has emerged as a promising approach to address these concerns by enabling collaborative model training across multiple decentralized institutions without sharing sensitive patient data. In this paper, we propose a new approach for reconstructing MRI using federated learning, aiming to achieve both high reconstruction accuracy and data privacy preservation. First, we create a local generative adversarial network to generate a high quality synthesized MRI using latent variables and noise via an adversarial model. Then, the local weights are aggregated at the server as a global generator to generalize images across multi institutions without sharing the data. Hence, this ensures privacy-preserving. Finally, we conduct experiments on different datasets to compare our model performance with other available methods.