We consider a poromechanics model including frictionless contact mechanics. The resulting model is the Biot equation with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to a linear parabolic flow equation. We propose a fully discrete iterative scheme for solving this model, extending the fixed-stress splitting scheme. We use finite elements in space and a backward Euler discretization in time. We show that the fixed stress split scheme is a contraction.