In the present work, the CO oxidation rate on size-selected Pd clusters supported on thin MgO films is investigated in pulsed molecular beam experiments. By varying the cluster coverage independent of the cluster size, we were able to change the ratio of direct and diffusion flux (reverse spill-over) of CO onto the cluster catalyst and thus probe the influence of reverse spill-over on the reaction rate for different cluster sizes (Pd-8 and Pd-30). The experimental results show that the change in reaction rate as a function of cluster coverage is different for Pd-8 and Pd-30. In order to explain these findings, the CO flux onto the clusters is modeled utilizing the collection zone model for the given experimental conditions. The results indicate that, for small clusters (Pd-8), the reaction probability of an impinging CO molecule is independent of whether it is supplied by diffusion or direct flux. By contrast, for larger clusters (Pd-30) a reduced reaction probability is found for CO supplied by reverse spill-over compared to CO supplied by direct flux.