Despite the success of large language models (LLMs) across domains, their potential for efficient channel state information (CSI) compression and feedback in frequency division duplex (FDD) massive multiple-input multiple-output (mMIMO) systems remains largely unexplored yet increasingly important. In this paper, we propose a novel LLM-based framework for CSI feedback to exploit the potential of LLMs. We first reformulate the CSI compression feedback task as a masked token prediction task that aligns more closely with the functionality of LLMs. Subsequently, we design an information-theoretic mask selection strategy based on self-information, identifying and selecting CSI elements with the highest self-information at the user equipment (UE) for feedback. This ensures that masked tokens correspond to elements with lower self-information, while visible tokens correspond to elements with higher self-information, thus maximizing the accuracy of LLM predictions.