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Asynchronous learning protocols have regained attention lately, especially in the Federated Learning (FL) setup, where slower clients can severely impede the learning process. Herein, we propose \texttt{AsyncDrop}, a novel asynchronous FL framework that utilizes dropout regularization to handle device heterogeneity in distributed settings. Overall, \texttt{AsyncDrop} achieves better performance compared to state of the art asynchronous methodologies, while resulting in less communication and training time overheads. The key idea revolves around creating ``submodels'' out of the global model, and distributing their training to workers, based on device heterogeneity. We rigorously justify that such an approach can be theoretically characterized. We implement our approach and compare it against other asynchronous baselines, both by design and by adapting existing synchronous FL algorithms to asynchronous scenarios. Empirically, \texttt{AsyncDrop} reduces the communication cost and training time, while matching or improving the final test accuracy in diverse non-i.i.d. FL scenarios.