The 3D stacking of various 2D systems is an intelligent way of aiming to overcome the limitations usually faced by 2D systems. We study the adsorption of graphene on noble metal monolayers upon Ni (111) substrate, using density functional theory. The bonding mechanism at noble metal-graphene and noble metal-Ni interfaces is found to be physisorption and chemisorption, respectively. The bonding of graphene to Cu, Ag, and Au (111) monolayers is so weak that the conical shape of the Dirac point is preserved. The doping effects of a substrate lead to a small opening gap for gr/Cu/Ni and gr/Ag/Ni systems. These predictions are in agreement with experimental results. The intercalation of a noble metal monolayer between graphene and Ni (111) substrate changes the magnetic response from Ni surface and causes the formation of a ferrimagnetic system.