In the paper is proposed a dq model predictive control (MPC) for an induction machine (IM) drive. The inner current plant has a multi-input multi-output (MIMO) nonlinear model, with a strong coupling structure. To obtain a single-input single-output (SISO) structure, the MIMO current model is decoupled by a feedforward technique, resulting in two independent SISO models that correspond to the dynamics of the R-L equivalent circuits. The linear MPC current controller is designed for the two SISO resulted models, obtaining an optimal control law, adopting constraints imposed from physical limitations. The optimal current references are obtained via maximum torque per ampere (MTPA) strategy. Thus, in the outer speed loop due to the electromagnetic torque, the plant is nonlinear. For the outer loop, a linear MPC controller will be also used designed by employing a linear model of the outer plant obtained with the nominal value of the d-axis current in the torque expression. In order not to have steady state errors due to parameter mismatch, the reference applied to the speed controller will be a filtered one. A comparative analysis of the results obtained by linear MPC and PI laws shows the effectiveness of the first strategy.