We present a catalog of potential candidates for asteroid mass determination based on mutual close encounters of numbered asteroids with massive perturbers (D>20 km). Using a novel geometric approach tuned to optimize observability, we predict optimal epochs for mass determination observations. In contrast to previous studies that often used simplified dynamical models, we have numerically propagated the trajectories of all numbered asteroids over the time interval from 2013 to 2023 using relativistic equations of motion including planetary perturbations, J2 of the Sun, the 16 major asteroid perturbers and the perturbations due to non-sphericities of the planets. We compiled a catalog of close encounters between asteroids where the observable perturbation of the sky plane trajectory is greater than 0.5 mas so that astrometric measurements of the perturbed asteroids in the Gaia data can be leveraged. The catalog v1.0 is available at ftp://dosya.akdeniz.edu.tr/ivantsov.