In the present paper, it is introduced a category Wor the objects of which are affine smooth varieties over a field k and morphisms are certain variants of finite correspondences. A presheaf of Abelian groups with Witt-transfers is by definition a presheaf of Abelian groups on the category Wor. The homotopy invariance of the Nisnevich sheaf associated with an arbitrary homotopy invariant presheaf with Witt-transfers is proved. To construct a category of Witt-motives one should prove the homotopy invariance of Nisnevich cohomology of an arbitrary homotopy invariant Nisnevich sheaf with Witt-transfers.