We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes
flow. To be precise we add a multiple of the Ginzburg{Landau
energy as a regularization to the objective functional and relax the non-permeability of the medium outside the
fluid region. The resulting diffuse interface problem can be
shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers
and the optimality conditions. Additionally, we can derive a necessary optimality system for the sharp interface problem by geometric variations without stating additional regularity assumptions on the minimizing set.