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In this paper, a novel model predictive control (MPC) formulation has been proposed to solve tracking problems, considering a generalized offset cost function. Sufficient conditions on this function are given to ensure the local optimality property. This novel formulation allows to consider as target operation points, states which may be not equilibrium points of the linear systems. In this case, it is proved in this paper that the proposed control law steers the system to an admissible steady state (different to the target) which is optimal with relation to the offset cost function. Therefore, the proposed controller for tracking achieves an optimal closed-loop performance during the transient as well as an optimal steady state in case of not admissible target. These properties are illustrated in an example.