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We consider a federated learning framework in which a parameter server (PS) trains a global model by using $n$ clients without actually storing the client data centrally at a cloud server. Focusing on a setting where the client datasets are fast changing and highly temporal in nature, we investigate the timeliness of model updates and propose a novel timely communication scheme. Under the proposed scheme, at each iteration, the PS waits for $m$ available clients and sends them the current model. Then, the PS uses the local updates of the earliest $k$ out of $m$ clients to update the global model at each iteration. We find the average age of information experienced by each client and numerically characterize the age-optimal $m$ and $k$ values for a given $n$. Our results indicate that, in addition to ensuring timeliness, the proposed communication scheme results in significantly smaller average iteration times compared to random client selection without hurting the convergence of the global learning task.