Resource-constrained organizations with vast datasets often face significant challenges in training and fine-tuning large language models (LLMs) due to privacy and compliance requirements. These organizations cannot share their sensitive data but still require external computational resources for model creation. In this paper, we investigate the effectiveness of split learning (SL) techniques for fine-tuning LLMs while maintaining data privacy. We compare three strategies: a centralized approach, where all fine-tuning occurs on a central server, and two split learning strategies (plain and U-shaped), where fine-tuning is distributed between a client and a cloud server, ensuring the client retains control over sensitive data. The U-shaped strategy enhances the plain split learning approach by ensuring labels are not shared with the server, offering stronger privacy protection. Our experiments empirically evaluate these methods, comparing model quality and training efficiency. The results show that all three strategies achieve comparable model performance, evaluated using the loss metric. Although the U-shaped SL incurs higher network transmission costs, it provides enhanced privacy guarantees. This presents a trade-off between privacy and communication efficiency, making U-shaped SL a strong candidate for privacy-preserving LLM fine-tuning in resource-constrained environments.