Several subsurface technologies involve injection of fluids at high pressure. An example is the extraction of the unconventional resources which involves well-stimulation techniques. One of the main well-stimulation techniques, especially for tight shale gas formations, is hydraulic fracturing. During this process, a fluid is injected into the formation at an extremely high pressure to initiate a network of fractures. The generated fractures are assumed to remain open, but this is not always the case. To accurately model the situation when fractures close back, one has to consider a coupled flow with geomechanics problem along with contact mechanics boundary conditions. Motivated by that, in this work, we extend the well-known single rate and multirate fixed-stress split coupling scheme to include frictionless contact mechanics boundary conditions for a poroelastic Biot model. In this model, a frictionless contact is assumed with the well-known Signorini condition in a form with a gap function. We state the results on the convergence of the extended single rate and multirate fixed-stress split schemes based on a fixed-point Banach contraction argument giving rise to the linear convergence of the corresponding scheme.