The rapid evolution of Large Language Models (LLMs) underscores the critical importance of ethical considerations and data integrity in AI development, emphasizing the role of FAIR (Findable, Accessible, Interoperable, Reusable) data principles. While these principles have long been a cornerstone of ethical data stewardship, their application in LLM training data is less prevalent, an issue our research aims to address. Our study begins with a review of existing literature, highlighting the significance of FAIR principles in data management for model training. Building on this foundation, we introduce a novel framework that incorporates FAIR principles into the LLM training process. A key aspect of this approach is a comprehensive checklist, designed to assist researchers and developers in consistently applying FAIR data principles throughout the model development lifecycle. The practicality and effectiveness of our framework are demonstrated through a case study that involves creating a FAIR-compliant dataset to detect and reduce biases. This case study not only validates the usefulness of our framework but also establishes new benchmarks for more equitable, transparent, and ethical practices in LLM training. We offer this framework to the community as a means to promote technologically advanced, ethically sound, and socially responsible AI models.