The rise of Large Language Models (LLMs) has affected various disciplines that got beyond mere text generation. Going beyond their textual nature, this project proposal aims to investigate the interaction between LLMs and non-verbal communication, specifically focusing on gestures. The proposal sets out a plan to examine the proficiency of LLMs in deciphering both explicit and implicit non-verbal cues within textual prompts and their ability to associate these gestures with various contextual factors. The research proposes to test established psycholinguistic study designs to construct a comprehensive dataset that pairs textual prompts with detailed gesture descriptions, encompassing diverse regional variations, and semantic labels. To assess LLMs' comprehension of gestures, experiments are planned, evaluating their ability to simulate human behaviour in order to replicate psycholinguistic experiments. These experiments consider cultural dimensions and measure the agreement between LLM-identified gestures and the dataset, shedding light on the models' contextual interpretation of non-verbal cues (e.g. gestures).