Predicting future human pose is a fundamental application for machine intelligence, which drives robots to plan their behavior and paths ahead of time to seamlessly accomplish human-robot collaboration in real-world 3D scenarios. Despite encouraging results, existing approaches rarely consider the effects of the external scene on the motion sequence, leading to pronounced artifacts and physical implausibilities in the predictions. To address this limitation, this work introduces a novel multi-modal sense-informed motion prediction approach, which conditions high-fidelity generation on two modal information: external 3D scene, and internal human gaze, and is able to recognize their salience for future human activity. Furthermore, the gaze information is regarded as the human intention, and combined with both motion and scene features, we construct a ternary intention-aware attention to supervise the generation to match where the human wants to reach. Meanwhile, we introduce semantic coherence-aware attention to explicitly distinguish the salient point clouds and the underlying ones, to ensure a reasonable interaction of the generated sequence with the 3D scene. On two real-world benchmarks, the proposed method achieves state-of-the-art performance both in 3D human pose and trajectory prediction. More detailed results are available on the page: https://sites.google.com/view/cvpr2024sif3d.