Context. It will soon become possible to directly link the most accurate radio reference frame with the Gaia optical reference frame using many common extragalactic objects. It is important to know the level of coincidence between the radio and optical positions of compact active galactic nuclei (AGN). Aims. Using the best catalogues available at present, we investigate how many AGN with significantly large optical-radio positional offsets exist as well as the possible causes of these offsets. Methods. We performed a case study by finding optical counterparts to the International Celestial Reference Frame (ICRF2) radio sources in the Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9). The ICRF2 catalogue was used as a reference because the radio positions determined by Very Long Baseline Interferometry (VLBI) observations are about two orders of magnitude more accurate than the optical positions. Results. We find 1297 objects in common for ICRF2 and SDSS DR9. Statistical analysis of the optical-radio differences verifies that the SDSS DR9 positions are accurate to ~55 mas in both coordinates, with no systematic offset with respect to ICRF2. We find 51 sources (~4% of the sample) for which the positional offset exceeds 170 mas (~3{sigma}). Astrophysical explanations must exist for most of these outliers. There are 3 known strong gravitational lenses among them. Dual AGN or recoiling supermassive black holes may also be possible. Conclusions. The most accurate Gaia-VLBI reference frame link will require a careful selection of a common set of objects by eliminating the outliers. On the other hand, the significant optical-radio positional non-coincidences may offer a new tool for finding e.g. gravitational lenses or dual AGN candidates. Detailed follow-up radio interferometric and optical spectroscopic observations are encouraged to investigate the outlier sources found in this study.
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