Central cluster galaxies are the largest and most massive galaxies in the Universe. Although they host very old stellar populations, several studies found the existence of blue cores in some BCGs indicating ongoing star formation. We analyse VLT/X-Shooter stacked spectra of 6 nearby massive central galaxies with high central velocity dispersions (σ > 300 km s-1) at different galactocentric distances. We quantify the young stellar population out to 4 kpc by fitting near-UV and optical absorption line indices with predictions of composite stellar populations modelled by an old and a young stellar component. We also use IMF-sensitive indices since these galaxies have been found to host a bottom-heavy IMF in their central regions. We derive negative young stellar populations gradients, with mass fractions of stars younger than 1 Gyr decreasing with galactocentric distance, from 0.70 per cent within 0.8 kpc to zero beyond 2 kpc. We also measure the mass fraction in young stars for individual galaxies in the highest S/N central regions. All the galaxies have young components of less than one percent. Our results clearly suggest that the star formation in massive central cluster galaxies takes place in their galaxy cores (<2 kpc), which, with deeper gravitational potential wells, are capable of retaining more gas. Among the possible sources for the gas required to form these young stars, our results are consistent with an in situ origin via stellar evolution, which is sufficient to produce the observed young stellar populations.