The ability to anticipate human-object interactions is highly desirable in an intelligent assistive system in order to guide users during daily life activities and understand their short and long-term goals. Creating systems with such capabilities requires to approach several complex challenges. This work addresses the problem of human-object interaction anticipation in Egocentric Vision using Vision Large Language Models (VLLMs). We tackle key limitations in existing approaches by improving visual grounding capabilities through Set-of-Mark prompting and understanding user intent via the trajectory formed by the user's most recent gaze fixations. To effectively capture the temporal dynamics immediately preceding the interaction, we further introduce a novel inverse exponential sampling strategy for input video frames. Experiments conducted on the egocentric dataset HD-EPIC demonstrate that our method surpasses state-of-the-art approaches for the considered task, showing its model-agnostic nature.