We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co^{2+} ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na_{3}Co_{2}SbO_{6} as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20 meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.