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An adaptation of the WKB method in the deformation quantization formalism ispresented with the aim to obtain an approximate technique of solving theeigenvalue problem for energy in the phase space quantum approach. Arelationship between the phase $\sigma(\vec{r})$ of a wave function $\exp\left(\frac{i}{\hbar} \sigma(\vec{r}) \right)$ and its respective Wignerfunction is derived. Formulas to calculate the Wigner function of a product andof a superposition of wave functions are proposed. Properties of a Wignerfunction of interfering states are also investigated. Examples of this quasi -classical approximation in deformation quantization are analysed. A strict formof the Wigner function for states represented by tempered generalised functionshas been derived. Wigner functions of unbound states in the Poeschl - Tellerpotential have been found.

The Wentzel - Kramers - Brillouin approximation method applied to the Wigner function