We present a conceptual design of an inattention management middleware with adaptive target saliency. The design objective is to provide mechanisms for managing operator inattention in multi-display multitasking applications. The conceptual design integrates ideas from situational awareness into its mechanisms to provide dynamic target saliency as a means to 1) guide operators through sub-tasks by drawing attention to high priority targets; and 2) guide operators on how to efficiently split their attention between tasks. We motivate the design by analysis of the results following a formative study with a prototype version of the conceptual design.