Context. The Ophiuchus cloud complex is one of the best laboratories to study the earlier stages of the stellar and protoplanetary disc evolution. The wealth of accurate astrometric measurements contained in the Gaia Data Release 2 can be used to update the census of Ophiuchus member candidates. Aims. We seek to find potential new members of Ophiuchus and identify those surrounded by a circumstellar disc. Methods. We constructed a control sample composed of 188 bona fide Ophiuchus members. Using this sample as a reference we applied three different density-based machine learning clustering algorithms (DBSCAN, OPTICS, and HDBSCAN) to a sample drawn from the Gaia catalogue centred on the Ophiuchus cloud. The clustering analysis was applied in the five astrometric dimensions defined by the three-dimensional Cartesian space and the proper motions in right ascension and declination. Results. The three clustering algorithms systematically identify a similar set of candidate members in a main cluster with astrometric properties consistent with those of the control sample. The increased flexibility of the OPTICS and HDBSCAN algorithms enable these methods to identify a secondary cluster. We constructed a common sample containing 391 member candidates including 166 new objects, which have not yet been discussed in the literature. By combining the Gaia data with 2MASS and WISE photometry, we built the spectral energy distributions from 0.5 to 22 μm for a subset of 48 objects and found a total of 41 discs, including 11 Class II and 1 Class III new discs. Conclusions. Density-based clustering algorithms are a promising tool to identify candidate members of star forming regions in large astrometric databases. By combining the Gaia data with infrared catalogues, it is possible to discover new protoplanetary discs. If confirmed, the candidate members discussed in this work would represent an increment of roughly 40–50% of the current census of Ophiuchus.