We study texture zeros of Dirac mass matrix in a minimal inverse seesaw (2, 3) model with \(S_4\) flavor symmetry. The seesaw model is extended with the addition of two right-handed neutrinos and three sterile states in intermediate mass range. The structure of the mass matrices is obtained from \(S_4\) symmetry. There are six possible two zero textures of the Dirac mass matrix. We study the neutrino mass and mixing within the six different textures emphasizing Dirac CP phase and the mixing angle \(\theta _{23}\) that may shed light on octant problem. Based on the allowed ranges of the mass and mixing with the active neutrinos, we study the viability of the different textures.