The state-of-the-art face recognition systems are typically trained on a single computer, utilizing extensive image datasets collected from various number of users. However, these datasets often contain sensitive personal information that users may hesitate to disclose. To address potential privacy concerns, we explore the application of federated learning, both with and without secure aggregators, in the context of both supervised and unsupervised face recognition systems. Federated learning facilitates the training of a shared model without necessitating the sharing of individual private data, achieving this by training models on decentralized edge devices housing the data. In our proposed system, each edge device independently trains its own model, which is subsequently transmitted either to a secure aggregator or directly to the central server. To introduce diverse data without the need for data transmission, we employ generative adversarial networks to generate imposter data at the edge. Following this, the secure aggregator or central server combines these individual models to construct a global model, which is then relayed back to the edge devices. Experimental findings based on the CelebA datasets reveal that employing federated learning in both supervised and unsupervised face recognition systems offers dual benefits. Firstly, it safeguards privacy since the original data remains on the edge devices. Secondly, the experimental results demonstrate that the aggregated model yields nearly identical performance compared to the individual models, particularly when the federated model does not utilize a secure aggregator. Hence, our results shed light on the practical challenges associated with privacy-preserving face image training, particularly in terms of the balance between privacy and accuracy.