In a recent publication [R.G. Parr and S. Liu, Chem. Phys. Lett. 267, 164(1997)], it has been argued that the total electron-electron repulsion energy density functional Veetp] can be expressed as a sum of functionals homogeneous of degrees one and two, with respect to density scaling. In this paper, starting from the Levy-Perdew virial relation, we demonstrate that one of the components of Vee[ρ], the exchange energy density functional Ex[ρ], can be expressed reasonably well in this way in a simple form. Namely, Ex[ρ] can be expressed as a linear combination of the classical electron-electron repulsion J[ρ] and the various electrostatic potentials at nuclei due to the electrons. Numerical tests are made for atoms, ions, and a few molecules. Good agreement between the accurate and the estimated exchange energies is observed.