  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 ($\rm {f_{gas}}$) and star formation
efficiency ($\rm {SFE}$) are responsible for quenching green valley galaxies at
all radii: both quantities are suppressed with respect to typical star-forming
regions. $\rm {f_{gas}}$ and $\rm {SFE}$ 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 $\rm
{f_{gas}}$ is reduced by $\rm \sim 1~dex$ in the central regions, but the star
formation rate is too low to be measured, leading to upper limits for the $\rm
{SFE}$. Moving from the outer disc to central regions, the reduction in $\rm
{f_{gas}}$ is driven by an increasing $\rm \Sigma_{\star}$ profile rather than
a decreasing $\rm \Sigma_{H_{2}}$ profile. The reduced $\rm {f_{gas}}$ 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 $\rm {f_{gas}}$ may be deceiving in
inferring the cause of quenching, particularly in the central (bulge-dominated)
regions of galaxies.
