This paper presents a novel Model Predictive Control (MPC) algorithm for Linear Parameter Varying (LPV) systems represented in the Input-Output (IO) form. The proposed MPC is derived using estimates for the future scheduling parameter trajectory, made viable through a recursive Taylor-based extrapolation law. The method also includes explicit integral action, which, coupled with quadratic terminal ingredients, enables offset-free reference tracking and asymptotic IO stability. A numeric benchmark example is used to illustrate the advantages of the proposed method, as well as its real-time capabilities.