In this paper, we propose a novel framework that leverages large language models (LLMs) for predicting missing values in time-varying graph signals by exploiting spatial and temporal smoothness. We leverage the power of LLM to achieve a message-passing scheme. For each missing node, its neighbors and previous estimates are fed into and processed by LLM to infer the missing observations. Tested on the task of the online prediction of wind-speed graph signals, our model outperforms online graph filtering algorithms in terms of accuracy, demonstrating the potential of LLMs in effectively addressing partially observed signals in graphs.