Federated Learning (FL) offers a decentralized framework that preserves data privacy while enabling collaborative model training across distributed clients. However, FL faces significant challenges due to limited communication resources, statistical heterogeneity, and the need for balanced client participation. This paper proposes an Age of Information (AoI)-based client selection policy that addresses these challenges by minimizing load imbalance through controlled selection intervals. Our method employs a decentralized Markov scheduling policy, allowing clients to independently manage participation based on age-dependent selection probabilities, which balances client updates across training rounds with minimal central oversight. We provide a convergence proof for our method, demonstrating that it ensures stable and efficient model convergence. Specifically, we derive optimal parameters for the Markov selection model to achieve balanced and consistent client participation, highlighting the benefits of AoI in enhancing convergence stability. Through extensive simulations, we demonstrate that our AoI-based method, particularly the optimal Markov variant, improves convergence over the FedAvg selection approach across both IID and non-IID data settings by $7.5\%$ and up to $20\%$. Our findings underscore the effectiveness of AoI-based scheduling for scalable, fair, and efficient FL systems across diverse learning environments.