The European space mission Gaia to be launched this autumn will perform astrometric observation of small Solar system bodies with precision of 0.3-5 mas. Thus, it should allow determination of masses for large asteroids by dynamical method which is by measuring perturbation effects produced by larger asteroids on the motion of smaller ones passing by. As far as Gaia will not be able to observe the maximum perturbation effect to be occurred before the probe launch, but will observe the lesser perturbing effect after this event, the possible solution is to make ground-based observations of selected perturbed asteroids beforehand and then to link them with the Gaia observations. The predictions of such encounters between asteroids were made from 1-1-2013 till 1-1-2015. We have found more than 800 encounters of all presently known 360,190 asteroids with the largest 50 asteroids. This project will allow to significantly increase the number of large asteroids for which Gaia will produce masses.