Recent results indicate a correlation between nuclear radio loudness of active galaxies and their central stellar surface-brightness profiles, in that ‘core’ galaxies (with inner logarithmic slope γ≤ 0.3) are significantly more radio loud than ‘power-law’ galaxies (γ≥ 0.5). This connection, which indicates possible links between radio loudness and galaxy formation history (e.g. through black hole spin), has so far only been confirmed for a radio-selected sample of galaxies. Furthermore, it has since been shown that the Nuker law, which was used to parametrize the brightness profiles in these studies, gives a poor description of the brightness profile, with its parameters varying systematically with the radial fitted extent of the profile. Here, we present an analysis of the central surface brightness profiles of the active galaxies of Hubble type T≤ 3, that were identified by the optically selected Palomar spectroscopic survey of nearby galaxies. We fit the brightness profiles using Sérsic, Core-Sérsic and, where necessary, Double-Sérsic models, which we fit to the semimajor axis brightness profiles extracted from high-resolution images of the galaxies from the Hubble Space Telescope. We use these fits to classify the galaxies as ‘Core’, ‘Sérsic’ or ‘Double-Sérsic’. We compare the properties of the active galactic nuclei (AGN) and their host galaxies with this classification, and we recover the already established trend for Core galaxies to be more luminous and contain a higher mass supermassive black hole. Defining the radio loudness of an AGN as the ratio of the nuclear radio luminosity to [O iii] line luminosity, which allows us to include most of the AGN in our sample and prevents a bias against dim nuclei that are harder to extract from the brightness profiles, we find that AGN hosted in Core galaxies are generally more radio loud than those hosted in Sérsic galaxies, although there is a large overlap between the two subsamples. The correlation between radio loudness and brightness profile can partly be explained by a correlation between radio loudness and black hole mass. Additionally, there is a significant (99 per cent confidence) partial correlation between radio loudness and the Core/Sérsic classification of the host galaxy, which lends support to the previous results based on the radio-selected sample, although it is possible that this partial correlation arises because AGN in core galaxies tend to have a lower accretion rate as well as a higher central black hole mass.