Chemical ordering in magic-size Ag-Pd nanoalloys is studied by means of global optimization searches within an atomistic potential developed on the basis of density functional theory calculations. Ag-rich, intermediate and Pd-rich compositions are considered for fcc truncated octahedral, icosahedral and decahedral geometric structures. Besides a surface enrichment in Ag, we find a significant subsurface enrichment in Pd, which persists to quite high temperatures as verified by Monte Carlo simulations. This subsurface Pd enrichment is stronger in nanoparticles than in bulk systems and is rationalized in terms of the energetics of the inclusion of a single Pd impurity in an Ag host nanoparticle. Our results can be relevant to the understanding of the catalytic activity of Ag-Pd nanoparticles in those reactions in which subsurface sites play a role.