This paper presents a stator flux linkage estimation method for synchronous machines (SMs) using a finite control set model predictive control (FCS-MPC). The key idea is that the integration error in a circular motion in the stationary frame is estimated and leverages the stator flux linkages by subtracting the estimation of the integration error from the integration result. The integration error can be directly calculated by this motion equation in the time domain. The proposed method is verified through MATLAB simulation results obtained using a 35-kW SM drive.