Heterogeneous nucleation in solutions on planar solid surfaces is modeled taking into account changes of the state parameters of the critical clusters in dependence on supersaturation. The account of the variation of the state parameters of the cluster phase on nucleation is performed in the framework of the generalized Gibbs' approach. A regular solution is chosen as a model for the analysis of the basic qualitative characteristics of the process. It is shown that, employing the generalized Gibbs approach, contact angle and catalytic activity factor for heterogeneous nucleation become dependent on the degree of metastability (supersaturation) of the solution. For the case of formation of a cluster in supersaturated solutions on a surface of low wettability (the macroscopic equilibrium contact angles being larger than 90°), the solid surface has only a minor influence on nucleation. In the alternative case of high wettability (for macroscopic equilibrium contact angles being less than 90°), nucleation is significantly enhanced by the solid surface. Effectively, the existence of the solid surface results in a significant shift of the spinodal to lower supersaturations as compared with homogeneous nucleation. Qualitatively, the same behavior is observed now near the new (solid surface induced) limits of instability of the solution as compared with the behavior near to the spinodal curve in the case of homogeneous nucleation.