The recent discoveries of gravitational wave events and in one case also its electromagnetic (EM) counterpart allow us to study the Universe in a novel way. The increased sensitivity of the LIGO and Virgo detectors has opened the possibility for regular detections of EM transient events from mergers of stellar remnants. Gravitational wave sources are expected to have sky localisation up to a few hundred square degrees, thus Gaia as an all-sky multi-epoch photometric survey has the potential to be a good tool to search for the EM counterparts. In this paper we study the possibility of detecting EM counterparts to gravitational wave sources using the Gaia Science Alerts system. We develop an extension to current used algorithms to find transients and test its capabilities in discovering candidate transients on a sample of events from the observation periods O1 and O2 of LIGO and Virgo. For the gravitational wave events from the current run O3 we expect that about 16 (25) per cent should fall in sky regions observed by Gaia 7 (10) days after gravitational wave. The new algorithm will provide about 21 candidates per day from the whole sky.