We have fitted the Mg2 absorption index gradients for 21 brightest cluster galaxies (BCGs), in the nearby Universe, for which we have obtained high signal-to-noise ratio, long-slit spectra on the Gemini telescopes. This is a subsample of a large optical, spatially resolved, spectroscopic sample of BCGs which allows possible connections between the kinematical, dynamical and stellar population properties to be studied. We find a weak correlation between the Mg2 gradients and central velocity dispersion, with gradients becoming steeper with increasing mass. An equivalent correlation for normal ellipticals in the same mass range is not found, suggesting that the BCG stellar population profiles are shaped by mechanisms related to the potential well of the cluster where they live. This suggestion is reinforced by the existence of a correlation between the Mg2 gradients and the BCG distance to the X-ray peak luminosity of the cluster. ; http://dx.doi.org/10.1111/j.1365-2966.2011.18909.x ; http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2011.18909.x/pdf