Context . Strongly lensed quasars are fundamental sources for cosmology. The Gaia space mission covers the entire sky with the unprecedented resolution of 0.18″ in the optical, making it an ideal instrument to search for gravitational lenses down to the limiting magnitude of 21. Nevertheless, the previous Gaia Data Releases are known to be incomplete for small angular separations such as those expected for most lenses. Aims . We present the Data Processing and Analysis Consortium GravLens pipeline, which was built to analyse all Gaia detections around quasars and to cluster them into sources, thus producing a catalogue of secondary sources around each quasar. We analysed the resulting catalogue to produce scores that indicate source configurations that are compatible with strongly lensed quasars. Methods . GravLens uses the DBSCAN unsupervised clustering algorithm to detect sources around quasars. The resulting catalogue of multiplets is then analysed with several methods to identify potential gravitational lenses. We developed and applied an outlier scoring method, a comparison between the average BP and RP spectra of the components, and we also used an extremely randomised tree algorithm. These methods produce scores to identify the most probable configurations and to establish a list of lens candidates. Results . We analysed the environment of 3 760 032 quasars. A total of 4 760 920 sources, including the quasars, were found within 6″ of the quasar positions. This list is given in the Gaia archive. In 87% of cases, the quasar remains a single source, and in 501 385 cases neighbouring sources were detected. We propose a list of 381 lensed candidates, of which we identified 49 as the most promising ones. Beyond these candidates, the associate tables in this Focused Product Release allow the entire community to explore the unique Gaia data for strong lensing studies further.Read less <