Carbon diffusion in transition metal nanoparticles is assumed to be a key factor in the catalyzed growth of carbon nanotubes (CNT). Aiming at designing more efficient catalysts, we have compared this carbon diffusion process in the near surface and in the bulk of Ni and Ni(3)Pd by means of density functional theory (DFT) calculations. Ni nanoparticles are indeed the most largely used catalysts and the alloying with Pd could modify and improve their properties. The alloy has the same crystal structure as pure Ni, with a slight lattice expansion due to the presence of palladium. For both systems, the subsurface octahedral site is the most stable adsorption site, but the thermodynamic trend favoring the penetration to the subsurface is larger on the alloy than on the Ni. As a result, in the conditions of temperature and pressure for nanotube growth, the population of the subsurface sites is a more exothermic process on the alloy. In addition, while on pure nickel the diffusion over the (111) surface is easy, on the alloy the vertical process leading the carbon to the subsurface is preferred. Palladium atoms have the double effect to expand the lattice parameter providing more adapted diffusion channels for the carbon and to create new adsorption sites less stable than the all-nickel ones. The results can be related to more selective formation of nanotubes on the alloy at low temperature, where Ni produces fibers.