The correlation functional Ec[ρ] known in Levy's constrained search formulation of density functional theory is also one of the components of the energy functional in Frozen-Density Embedding Theory (FDET) [Wesolowski, Phys. Rev. A, 77 (2008) 012504] if the embedded wavefunction has the single determinant form. The relation between the FDET energy and quantities available from an auxiliary system is derived. In the auxiliary system, Ec[ρ] and its functional derivative (correlation potential) are entirely neglected. The relation is exact up to the quadratic terms density changes caused by electron-electron correlation. It is discussed in view of its practical applica- tions in modelling electronic structure of embedded species.