The paper presents a model predictive allocation scheme for constrained over-actuated linear systems, for which input redundancy entails the existence of multiple trajectories in the state space yielding a given reference output. The method relies upon the concept of inverse model allocation, where dynamic allocation of reference state and input trajectories is accomplished within the framework of output regulation while maintaining invariance of the error-zeroing subspace. The study focuses on the design of model predictive allocator to achieve constraint satisfaction and asymptotic evolution of the trajectories to a pre-computed steady-state target. In particular, the objective of this study is the analysis of the stability and feasibility properties of the proposed schemes and the characterization of suitable sufficient conditions for stability in geometric terms. In support of the theoretical findings, this study presents an example where the proposed methodology is applied to solve a constrained tracking control problem for the linearized model of the air path system of a turbocharged Diesel engine. (C) 2016 Elsevier Ltd. All rights reserved.