We study the connection between the BCS pairing model and the inhomogeneous vertex model. The two spectral problems coincide in the quasi-classical limit of the off-shell Bethe ansatz of the disordered six-vertex model. The latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the BCS model. A generating functional whose quasi-classical expansion leads to the constants of motion of the BCS model, and in particular the Hamiltonian, is identified.