Accurate determination of the nucleus composition during isothermal alloy solidification still represents a great challenge nowadays. In this paper, a kinetic scheme was added to the Hillert-Rettenmayr thermodynamic analysis of the deviation from local equilibrium at migrating phase interfaces. A so-called interface permeability was introduced to account for the unambiguous determination of the energy dissipation of the solute rearrangement at the liquid-solid interface and the driving force for interface movement, from which the nucleus composition can be then evaluated. After benchmark test, a pragmatic nucleation model for solidification was also proposed, and applied in three-dimensional phase-field simulations of nucleation and subsequent dendritic growth during isothermal solidification process in one hypothetic Al-Si alloy. Moreover, the influence of the interface permeability on nucleation rate was fully discussed by exploring its effect on the initial nucleus components and the corresponding nucleation driving force.