The catalytic properties of sub-nanometer Cun clusters are modified by interactions with inorganic supports used for their stabilization. In this work, the reactivity towards O2 dissociation of Cu5 and Cu7 clusters confined within the cavities of the CHA zeolite is theoretically investigated by means of periodic DFT calculations. Increasing the Al content in the zeolite framework not only modifies the cluster morphology, but also leads to a decrease in the electronic density available on the supported Cun clusters, which in turn leads to higher activation energies for O2 dissociation. Together with the cluster size and shape, the Si/Al ratio in the zeolite support appears as a potential parameter to finely tune the stability and oxidation properties of Cu-based catalysts.