The abundance of dark matter (DM) subhalos orbiting a host galaxy is a generic prediction of the cosmological framework, and is a promising way to constrain the nature of DM. In this paper, we investigate the use of machine learning-based tools to quantify the magnitude of phase-space perturbations caused by the passage of DM subhalos. A simple binary classifier and an anomaly detection model are proposed to estimate if stars or star particles close to DM subhalos are statistically detectable in simulations. The simulated datasets are three Milky Way-like galaxies and nine synthetic Gaia DR2 surveys derived from these. Firstly, we find that the anomaly detection algorithm, trained on a simulated galaxy with full 6D kinematic observables and applied on another galaxy, is nontrivially sensitive to the DM subhalo population. On the other hand, the classification-based approach is not sufficiently sensitive due to the extremely low statistics of signal stars for supervised training. Finally, the sensitivity of both algorithms in the Gaia-like surveys is negligible. The enormous size of the Gaia dataset motivates the further development of scalable and accurate data analysis methods that could be used to select potential regions of interest for DM searches to ultimately constrain the Milky Way's subhalo mass function, as well as simulations where to study the sensitivity of such methods under different signal hypotheses.