We present a study of the impact of a bright quasar on the redshifted 21-cm signal during the epoch of reionization (EoR). Using three different cosmological radiative transfer simulations, we investigate if quasars are capable of substantially changing the size and morphology of the H ii regions they are born in. We choose stellar and quasar luminosities in a way that is favourable to seeing such an effect. We find that even the most luminous of our quasar models is not able to increase the size of its native H ii region substantially beyond those of large H ii regions produced by clustered stellar sources alone. However, the quasar H ii region is found to be more spherical. We next investigate the prospects of detecting such H ii regions in the redshifted 21-cm data from the Low Frequency Array (LOFAR) by means of a matched filter technique. We find that H ii regions with radii ∼25 comoving Mpc or larger should have a sufficiently high detection probability for 1200 h of integration time. Although the matched filter can in principle distinguish between more and less spherical regions, we find that when including realistic system noise this distinction can no longer be made. The strong foregrounds are found not to pose a problem for the matched filter technique. We also demonstrate that when the quasar position is known, the redshifted 21-cm data can still be used to set upper limits on the ionizing photon rate of the quasar. If both the quasar position and its luminosity are known, the redshifted 21-cm data can set new constraints on quasar lifetimes.