Federated learning (FL) is increasingly adopted in domains like healthcare, where data privacy is paramount. A fundamental challenge in these systems is statistical heterogeneity-the fact that data distributions vary significantly across clients (e.g., different hospitals may treat distinct patient demographics). While current FL algorithms focus on aggregating model updates from these heterogeneous clients, the potential of the central server remains under-explored. This paper is motivated by a healthcare scenario: could a central server not only coordinate model training but also guide a new patient to the hospital best equipped for their specific condition? We generalize this idea to propose a novel paradigm for FL systems where the server actively guides the allocation of new tasks or queries to the most appropriate client. To enable this, we introduce a density ratio model and empirical likelihood-based framework that simultaneously addresses two goals: (1) learning effective local models on each client, and (2) finding the best matching client for a new query. Empirical results demonstrate the framework's effectiveness on benchmark datasets, showing improvements in both model accuracy and the precision of client guidance compared to standard FL approaches. This work opens a new direction for building more intelligent and resource-efficient FL systems that leverage heterogeneity as a feature, not just a bug. Code is available at https://github.com/zijianwang0510/FedDRM.git.