Context. Multiply imaged gravitationally lensed quasars are among the most interesting and useful observable extragalactic phenomena. Because their study constitutes a unique tool in various fields of astronomy, they are highly sought, but difficult to find. Even in this era of all-sky surveys, discovering them remains a great challenge, with barely a few hundred systems currently known. Aims: We aim to discover new multiply imaged quasar candidates in the recently published Gaia Data Release 2 (DR2), which is the astrometric and photometric all-sky survey with the highest spatial resolution that achieves effective resolutions from 0.4″ to 2.2″. Methods: We cross-matched a merged list of quasars and candidates with Gaia DR2 and found 1 839 143 counterparts within 0.5″. We then searched matches with more than two Gaia DR2 counterparts within 6″. We further narrowed the resulting list using astrometry and photometry compatibility criteria between the Gaia DR2 counterparts. A supervised machine-learning method, called extremely randomized trees, was finally adopted to assign a probability of being lensed to each remaining system. Results: We report the discovery of two quadruply imaged quasar candidates that are fully detected in Gaia DR2. These are the most promising new quasar lens candidates from Gaia DR2 and a simple singular isothermal ellipsoid lens model is able to reproduce their image positions to within 1 mas. This Letter demonstrates the discovery potential of Gaia for gravitational lenses.