The technical note presents the design of a reference governor that manages directly the state and input references for constrained output regulation problems. In particular, for the class of so-called weakly input redundant linear systems, the proposed method leads to a taxonomy in terms of non-intrusive and intrusive reference governors, on the basis of the effect of reference manipulation on the tracking error. Non-intrusive references constitute a degree of freedom that one can freely select to meet constraint requirements; intrusive references are also assignable during transient, but shall be forced to vanish in steady state in order to achieve exact regulation. A simulation study illustrates the features of the proposed approach in support of the theoretical findings.