Zero-shot Object Goal Navigation requires an embodied agent to locate a target object in an unseen environment, where the choice of which frontier to explore next is critical to both success and efficiency. Existing methods score frontiers from already-observed cues such as nearby objects or scene graphs, leaving the structure beyond each frontier implicit and offering no principled prior for choosing among rooms the agent has yet to see. In contrast, the hippocampal entorhinal system supports navigation through a predictive cognitive map that anticipates unseen space from partial observations. Inspired by this, we propose PredNav, which externalizes a hierarchical cognitive map with metric, instance-semantic, and topological layers, and casts frontier selection as room-level structured prediction over its topological layer. A language model infers the likely room type and target relevance behind each frontier, which is fused with CLIP visual evidence, an offline room category prior, and geodesic cost under phase-adaptive weights. A vision-language verifier then gates stop using direct visual evidence. Extensive experiments on MP3D and HM3D demonstrate the effectiveness of our method.