In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (vtnad(r)) needs to be approximated. Since vtnad(r) is defined as a bifunctional, the common strategies rely on approximating vtnad[ρA,ρB](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (ρA and ρB) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where ρA is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum ρA + ρB is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsäcker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities.