The Gaia mission provided to the scientific community astrometric solutions at an unprecedented precision. In the Gaia Data Release 2, there are more than 14.000 asteroids observed for over 230.000 transits. DR3 will overcome this number and provide data for more than 150.000 asteroids. More than 300 asteroids are known to have satellites today but a whole range of separation and size ratios is out of reach from the ground. Using the astrometry by Gaia we are working on a method to systematically search for the astrometric wobbling induced by possible satellites on the measured asteroid positions. We exploit period-search techniques on suitable observation sequences and use statistical approaches to determine the probability of fake signal detection. From our preliminary results, we find that we can detect reliable periodicities in the astrometric position for at least 1% of the bodies, paving the way to the first satellite discoveries by the astrometric technique. Periods found in literature obtained by photometry or the physical characteristics of the main body can provide further useful constraints on the potential satellite system.