ABSTRACT The star formation main sequence (SFMS) is a tight relation between the galaxy star formation rate (SFR) and its total stellar mass (M⋆). Early-type galaxies (ETGs) are often considered as low-SFR outliers of this relation. We study, for the first time, the separated distribution in the SFR versus M⋆ of bulges and discs of 49 ETGs from the CALIFA survey. This is achieved using c2d, a new code to perform spectrophotometric decompositions of integral field spectroscopy data cubes. Our results reflect that: (i) star formation always occurs in the disc component and not in bulges; (ii) star-forming discs in our ETGs are compatible with the SFMS defined by star-forming galaxies at z ∼ 0; (iii) the star formation is not confined to the outskirts of discs, but it is present at all radii (even where the bulge dominates the light); (iv) for a given mass, bulges exhibit lower sSFR than discs at all radii; and (v) we do not find a deficit of molecular gas in bulges with respect to discs for a given mass in our ETGs. We speculate our results favour a morphological quenching scenario for ETGs.