Federated Learning (FL) enables collaborative model building among a large number of participants without the need for explicit data sharing. But this approach shows vulnerabilities when privacy inference attacks are applied to it. In particular, in the event of a gradient leakage attack, which has a higher success rate in retrieving sensitive data from the model gradients, FL models are at higher risk due to the presence of communication in their inherent architecture. The most alarming thing about this gradient leakage attack is that it can be performed in such a covert way that it does not hamper the training performance while the attackers backtrack from the gradients to get information about the raw data. Two of the most common approaches proposed as solutions to this issue are homomorphic encryption and adding noise with differential privacy parameters. These two approaches suffer from two major drawbacks. They are: the key generation process becomes tedious with the increasing number of clients, and noise-based differential privacy suffers from a significant drop in global model accuracy. As a countermeasure, we propose a mixed-precision quantized FL scheme, and we empirically show that both of the issues addressed above can be resolved. In addition, our approach can ensure more robustness as different layers of the deep model are quantized with different precision and quantization modes. We empirically proved the validity of our method with three benchmark datasets and found a minimal accuracy drop in the global model after applying quantization.