ABSTRACT We study a sample of 48 127 galaxies selected from the SDSS MPA-JHU catalogue, with log M⋆/M⊙ = 10.73−11.03 and z < 0.1. Local galaxies in this stellar mass range have been shown to have systematically shorter assembly times within their inner regions (<0.5 R50) when compared to that of the galaxy as a whole, contrary to lower or higher mass galaxies that show consistent assembly times at all radii. Hence, we refer to these galaxies as Inside-Out Assembled Galaxy (IOAG) candidates. We find that the majority of IOAG candidates with well-detected emission lines are classified as either active galactic nucleus (AGN; 40 per cent) or composite (40 per cent) in the BPT (Baldwin, Phillips & Terlevich) diagram. We also find that the majority of our sources are located below the main sequence of star formation, and within the green valley or red sequence. Most BPT-classified star-forming IOAG candidates have spiral morphologies and are in the main sequence, whereas Seyfert 2 and composites have mostly spiral morphologies but quiescent star formation rates (SFRs). We argue that a high fraction of IOAG candidates seem to be in the process of quenching, moving from the blue cloud to the red sequence. Those classified as AGN have systematically lower SFRs than star-forming galaxies, suggesting that AGN activity may be related to this quenching. However, the spiral morphology of these galaxies remains in place, suggesting that the central star formation is suppressed before the morphological transformation occurs.