This work addresses the problem of tracking maneuvering objects with complex motion patterns, a task in which conventional methods often struggle due to their reliance on predefined motion models. We integrate a data-driven liquid neural network (LNN) into the random finite set (RFS) framework, leading to two LNN-RFS filters. By learning continuous-time dynamics directly from data, the LNN enables the filters to adapt to complex, nonlinear motion and achieve accurate tracking of highly maneuvering objects in clutter. This hybrid approach preserves the inherent multi-object tracking strengths of the RFS framework while improving flexibility and robustness. Simulation results on challenging maneuvering scenarios demonstrate substantial gains of the proposed hybrid approach in tracking accuracy.