Numerical simulation datasets used for non-intrusive reduced-order modelling for VIV problems, via sparse FOM inference (see https://arxiv.org/abs/2302.09981). The corresponding code is available via https://github.com/lgkimisis/VIV_sFOM_POD_inference. Snapshot data from the numerical simulation of two testcases are included, on the VIV dynamics for Re=90 and Re=180 flow over an elipse-shaped, non-deformable solid. The numerical simulation was performed via the Gascoigne3D open-source, monolithic FSI solver (https://doi.org/10.5281/zenodo.5574968).