The current efforts to find the materials hosting Kitaev model physics have been focused on Mott insulators of d^5 pseudospin-1/2 ions Ir^{4+} and Ru^{3+} with t_{2g}^5(S=1/2, L=1) electronic configuration. Here we propose that the Kitaev model can be realized in materials based on d^7 ions with t_{2g}^5e_g^2(S=3/2, L=1) configuration such as Co^{2+}, which also host the pseudospin-1/2 magnetism. Considering possible exchange processes, we have derived the d^7 pseudospin-1/2 interactions in 90^{circ} bonding geometry. The obtained Hamiltonian comprises the bond-directional Kitaev K and isotropic Heisenberg J interactions as in the case of d^5 ions. However, we find that the presence of additional, spin-active e_g electrons radically changes the balance between Kitaev and Heisenberg couplings. Most remarkably, we show that the exchange processes involving e_g spins are highly sensitive to whether the system is in Mott (U<Delta) or charge-transfer (U>Delta) insulating regime. In the latter case, to which many cobalt compounds do actually belong, the antiferromagnetic Heisenberg coupling J is strongly suppressed and spin-liquid phase can be stabilized. The results suggest cobalt-based materials as promising candidates for the realization of the Kitaev model.
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