This paper proposes a novel method for information management of a networked system for the purpose of efficient state estimation. Data shared between entities is transmitted over a common communication network. Based on the notion of Value of Information (Vol), we design a prioritizing scheduler in which systems determine the benefit of sharing their real-time data to improve state estimation accuracy. The system with the highest Vol is granted a time slot to provide its data. By using a rollout strategy, feasible algorithms are developed for computing the Vol-based priorities. For decoupled subsystems, performance certificates of the Vol-based strategy are derived. An automotive case study evaluates the proposed approach.