Hospital discharge delays are rooted in fragmented coordination across clinical, administrative, and logistical work. Discharge readiness depends on many interdependent tasks that must be completed in the correct sequence. No current system fully orchestrates discharge sub-tasks by reasoning across care plans, medication reconciliation, transport requests, follow-up scheduling, and pending orders in real time. Existing digital tools often support isolated functions rather than end-to-end coordination. This article proposes an agentic AI system that perceives discharge requirements, plans task sequences, executes coordination actions, and monitors completion under human supervision. The system is conceptual and should be understood as an emerging design pattern rather than an evaluated intervention. The proposed system includes a task decomposition engine, goal-oriented reasoning core, EHR data adapters, follow-up scheduling rules engine, transport request interfaces, and human override dashboard. These components would allow the agent to coordinate discharge logistics while preserving clinician authority. The system would function as a virtual discharge coordinator that continuously tracks task status and identifies stalled work. It could reduce idle coordination time, prevent overlooked tasks, and allow nurses and case managers to focus on higher-value clinical and relational work. Agentic AI could transform discharge management from a manual, interruption-prone process into an automated, accountable, and scalable workflow. Safe deployment would require interoperability, auditability, constrained autonomy, and rigorous evaluation.