This paper is devoted to the mathematical analysis of the contact capabilities of the fluid-structure interaction (FSI) model with seepage reported in [Comput. Methods Appl. Mech., 392:114637, 2022]. In the case of a rigid disk moving over a fixed horizontal plane, we show that this model encompasses contact and hence removes the non collision paradox of traditional FSI models which rely on Dirichlet or Dirichlet/Navier boundary conditions. Numerical evidence on the theoretical results is also provided.