We study the role of cold gas in quenching star formation in the green valley by analysing ALMA $^{12}$CO (1-0) observations of three galaxies with resolved optical spectroscopy from the MaNGA survey. We present resolution-matched maps of the star formation rate and molecular gas mass. These data are used to calculate the star formation efficiency (SFE) and gas fraction ($f_{rm~gas}$) for these galaxies separately in the central `bulge regions and outer disks. We find that, for the two galaxies whose global specific star formation rate (sSFR) deviates most from the star formation main sequence, the gas fraction in the bulges is significantly lower than that in their disks, supporting an `inside-out model of galaxy quenching. For the two galaxies where SFE can be reliably determined in the central regions, the bulges and disks share similar SFEs. This suggests that a decline in $f_{rm~gas}$ is the main driver of lowered sSFR in bulges compared to disks in green valley galaxies. Within the disks, there exist common correlations between the sSFR and SFE and between sSFR and $f_{rm~gas}$ on kpc scales -- the local SFE or $f_{rm~gas}$ in the disks declines with local sSFR. Our results support a picture in which the sSFR in bulges is primarily controlled by $f_{rm~gas}$, whereas both SFE and $f_{rm~gas}$ play a role in lowering the sSFR in disks. A larger sample is required to confirm if the trend established in this work is representative of green valley as a whole.
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