An approximation to the Kohn-Sham exchange potential (v(x)) in the Gross-Oliveira-Kohn theory of ensemble of states is proposed for excited states of atoms, making use of a coupled self-consistent fitting procedure to the parameters of an approximate potential generated from a nonlocal potential (v(x)(nonlocal)) coming from the Becke exchange energy density, the X-alpha(v(alpha)(X)) and the so-called short-ranged response potential (v(x)(resp)). The parameter values are obtained when the sum of the Coulomb and the approximate exchange potentials shows the least deviation from the analogous potential in the recently derived generalized Krieger-Li-Iafrate (KLI) approximation of the optimized potential method of ensembles. To test the quality of the proposed exchange potential, calculations are performed for the first two or three (excited-state) ensembles of Li, Be, Na, Mg, K, and Ca atoms and the ensemble energies and densities are compared with the ensemble KLI results. As the exact exchange potential is free from the ghost-interaction (i.e., the self-interaction between the elements of the ensemble) the proposed fitted potential reduces the ghost-interaction error as well. (C) 2003 American Institute of Physics.