ABSTRACT Scattering events with compact objects are expected in the primordial black hole (PBH) cold dark matter (CDM) scenario, due to close encounters between stars and PBHs in the dense environments of dwarf spheroidals. We develop a Bayesian framework to search for correlations among Milky Way stellar trajectories and those of globular clusters and dwarf galaxies in the halo and in other nearby galaxies. We apply the method to a selection of hypervelocity stars (HVS) and globular clusters from the Gaia DR2 catalogue and known nearby (mostly dwarf) galaxies with full phase-space and size measurements. We report positive evidence for trajectory intersection ∼20–40 Myr ago of up to two stars, depending on priors, with the Sagittarius dwarf spheroidal galaxy (dSph) when assuming the distance estimates of Marchetti, Rossi & Brown (2018). We verify that the result is compatible with their evolutionary status, setting a lower bound for their stellar age of ∼100 Myr. However, such scattering events are not confirmed when assuming Anders et al. (2019) distance estimates. We discuss shortcomings related to present data quality and future prospects for detection of HVS with the full Gaia catalogue and Sagittarius dSph.