The reference management algorithm is an auxiliary system which modifies the reference signal to fulfil the state and control constraints. In the previous works, most of such algorithms require the assumption that the state vector of the closed-loop system including the plant state is directly measurable, which may be unrealistic for some applications. In this paper, we develop a new reference management algorithm for discrete-time constrained systems with unmeasurable plant states. The present algorithm assures the constraints fulfilment when an ellipsoidal set of possible plant state vectors is available instead of the plant state itself. It is shown that the set of possible plant states can be obtained from the measured outputs by using the Luenberger-type observer or the set-valued observer. The effectiveness of the present method is demonstrated by a numerical example.