Affordance prediction, which identifies interaction regions on objects based on language instructions, is critical for embodied AI. Prevailing end-to-end models couple high-level reasoning and low-level grounding into a single monolithic pipeline and rely on training over annotated datasets, which leads to poor generalization on novel objects and unseen environments. In this paper, we move beyond this paradigm by proposing A4-Agent, a training-free agentic framework that decouples affordance prediction into a three-stage pipeline. Our framework coordinates specialized foundation models at test time: (1) a Dreamer that employs generative models to visualize how an interaction would look; (2) a Thinker that utilizes large vision-language models to decide what object part to interact with; and (3) a Spotter that orchestrates vision foundation models to precisely locate where the interaction area is. By leveraging the complementary strengths of pre-trained models without any task-specific fine-tuning, our zero-shot framework significantly outperforms state-of-the-art supervised methods across multiple benchmarks and demonstrates robust generalization to real-world settings.