Fluid–structure interaction (FSI) phenomena involving bluff bodies in cross-flow are governed by strongly nonlinear couplings between unsteady flow dynamics and structural motion, leading to vortex-induced vibrations, lock-in effects, and complex force responses. Accurately capturing these mechanisms typically relies on high-fidelity CFD-based simulations, whose computational cost limits their use in large parametric studies and repeated evaluations. In this context, data-driven reduced-order and surrogate modeling approaches based on machine learning have emerged as promising alternatives to accelerate FSI simulations. While recent methods have demonstrated encouraging results for data-driven reduced-order modeling of FSI systems, ensuring robust and stable long-term behavior in closed-loop fluid–structure coupling remains challenging, particularly in regimes involving strong nonlinear interactions and changes in flow–structure synchronization. The present work addresses this challenging problem by proposing a data-driven reduced-order modeling strategy aimed at capturing the coupled spatio-temporal dynamics of a spring-mounted circular cylinder in laminar cross-flow through a reduced-order representation combining latent flow variables and structural displacement. The approach, based on, combines a convolutional variational autoencoder for nonlinear dimensionality reduction of velocity and pressure fields with a recurrent neural network modeling the temporal evolution of the reduced-order state. The learned latent dynamics are coupled with a mass–spring structural model, enabling time-accurate closed-loop prediction of the fluid–structure response. Training data are generated using a high-fidelity lattice Boltzmann fluid solver (ProLB), with fluid–structure coupling handled via an immersed boundary method. Results show that the proposed reduced-order surrogate accurately reproduces dominant flow features, vortex shedding dynamics, and lift force evolution over multiple oscillation cycles when compared to high-fidelity ProLB simulations used as reference, while achieving a significant reduction in computational cost. These findings highlight the potential of data-driven reduced-order models for robust and efficient simulation of nonlinear, time-dependent multiphysics systems.