We analysed optical properties of giant radio quasars (with radio structures larger than 0.7 Mpc). To this day it is unclear why only a small fraction of radio sources attain such large sizes. There are a number of hypotheses attempting to explain this phenomenon, however the one treated in this paper has not yet been investigated in detail. This hypothesis assumes that the giant linear sizes of radio structures are due to internal properties of their central active galactic nuclei i.e. the specific properties of super-massive black holes and/or their accretion discs. We investigated whether a direct relation exists between the properties of the central "engine" and the origin of the Mpc scale radio structures. In our analysis, we did not find any relation between black hole mass and radio core power, however, we found a weak correlation between the accretion rate and radio core power. We also found a relation between a black hole's mass and linear size of the radio structure. The obtained results may suggest that giant radio quasars are similar to those of smaller size. There are also indications that giant radio quasars may be more evolved sources as compared with smaller radio quasars.