We study quenching in seven green valley galaxies on kpc scales by resolving their molecular gas content using \textsuperscript{12}CO(1-0) observations obtained with NOEMA and ALMA, and their star-formation rate using spatially resolved optical spectroscopy from the MaNGA survey. We perform radial stacking of both datasets to increase the sensitivity to molecular gas and star formation, thereby avoiding biases against strongly quenched regions. We find that both spatially resolved gas fraction ($fgas$) and star formation efficiency ($SFE$) are responsible for quenching green valley galaxies at all radii: both quantities are suppressed with respect to typical star-forming regions. $fgas$ and $SFE$ have roughly equal influence in quenching the outer disc. We are, however, unable to identify the dominant mechanism in the strongly quenched central regions. We find that $fgas$ is reduced by $\sim 1 dex$ in the central regions, but the star formation rate is too low to be measured, leading to upper limits for the $SFE$. Moving from the outer disc to central regions, the reduction in $fgas$ is driven by an increasing $\Sigma \star$ profile rather than a decreasing $\Sigma H2$ profile. The reduced $fgas$ may therefore be caused by a decrease in the gas supply rather than molecular gas ejection mechanisms, such as winds driven by active galactic nuclei. We warn more generally that studies investigating $fgas$ may be deceiving in inferring the cause of quenching, particularly in the central (bulge-dominated) regions of galaxies.