Federated Learning (FL) has gained attention across various industries for its capability to train machine learning models without centralizing sensitive data. While this approach offers significant benefits such as privacy preservation and decreased communication overhead, it presents several challenges, including deployment complexity and interoperability issues, particularly in heterogeneous scenarios or resource-constrained environments. Over-the-air (OTA) FL was introduced to tackle these challenges by disseminating model updates without necessitating direct device-to-device connections or centralized servers. However, OTA-FL brought forth limitations associated with heightened energy consumption and network latency. In this paper, we propose a multi-attribute client selection framework employing the grey wolf optimizer (GWO) to strategically control the number of participants in each round and optimize the OTA-FL process while considering accuracy, energy, delay, reliability, and fairness constraints of participating devices. We evaluate the performance of our multi-attribute client selection approach in terms of model loss minimization, convergence time reduction, and energy efficiency. In our experimental evaluation, we assessed and compared the performance of our approach against the existing state-of-the-art methods. Our results demonstrate that the proposed GWO-based client selection outperforms these baselines across various metrics. Specifically, our approach achieves a notable reduction in model loss, accelerates convergence time, and enhances energy efficiency while maintaining high fairness and reliability indicators.