ABSTRACT Exploiting the sample of 30 local star-forming, undisturbed late-type galaxies in different environments drawn from the GAs Stripping Phenomena in galaxies with MUSE (GASP), we investigate the spatially resolved star formation rate–mass ($\rm Σ _{SFR}$–$\rm Σ _*$) relation. Our analysis includes also the galaxy outskirts (up to >4 effective radii, re), a regime poorly explored by other Integral Field Spectrograph surveys. Our observational strategy allows us to detect H α out to more than 2.7re for 75 per cent of the sample. Considering all galaxies together, the correlation between the $\rm Σ _{SFR}$ and $\rm Σ _*$ is quite broad, with a scatter of 0.3 dex. It gets steeper and shifts to higher $\rm Σ _*$ values when external spaxels are excluded and moving from less to more massive galaxies. The broadness of the overall relation suggests galaxy-by-galaxy variations. Indeed, each object is characterized by a distinct $\rm Σ _{SFR}$ –$\rm Σ _*$ relation and in some cases the correlation is very loose. The scatter of the relation mainly arises from the existence of bright off-centre star-forming knots whose $\rm Σ _{SFR}$–$\rm Σ _*$ relation is systematically broader than that of the diffuse component. The $\rm Σ _{SFR}$–$\rm Σ _{tot \, gas}$ (total gas surface density) relation is as broad as the $\rm Σ _{SFR}$–$\rm Σ _*$ relation, indicating that the surface gas density is not a primary driver of the relation. Even though a large galaxy-by-galaxy variation exists, mean $\rm Σ _{SFR}$ and $\rm Σ _*$ values vary of at most 0.7 dex across galaxies. We investigate the relationship between the local and global SFR–M* relation, finding that the latter is driven by the existence of the size–mass relation.