Significant positional offsets of the value from 1 mas to more than 10mas were found previously between radio (VLBI) and optical (Gaia) positions of active galactic nuclei (AGNs). They happen preferentially parallel to the parsec-scale jet direction. AGNs with VLBI-to-Gaia offsets pointed downstream the jet are found to have favourably higher optical polarization, as expected if extended optical jets dominate in the emission and shift the Gaia centroid away from the physical nucleus of the source. Upstream offsets with the suggested domination of accretion discs manifest themselves through the observed low optical polarization. Direction of linear optical polarization is confirmed to preferentially align with parsec-scale jets in AGNs with dominant jets consistent with a toroidal magnetic field structure. Our findings support the disc-jet interpretation of the observed positional offsets. These results call on an intensification of AGN optical polarization monitoring programs in order to collect precious observational data. Taken together with the continued VLBI and Gaia observations, they will allow researchers to reconstruct detailed models of the disc-jet system in AGNs on parsec scales.