Missing data is a persistent challenge in clinical analysis, often undermining the reliability of machine learning models. This study explores the use of large language models (LLMs), both general-purpose and biomedical, for imputing missing values in the Pima Indians Diabetes Dataset. Patient records were reformulated as natural language prompts, with missing features posed as explicit questions to the models. We evaluated GPT-2, Llama-2-7B, BioBERT v1.1, Gemma-2-2B-it, Gemma-2-9B-it, and Bio-Medical-Llama-3-8B under Zero-Shot and Few-Shot prompting. While GPT-2, Llama-2-7B, and BioBERT showed limited performance, Gemma-2-9B-it and Bio-Medical-Llama-3-8B—especially with carefully designed Few-Shot prompts—produced accurate imputations and yielded downstream classification performance comparable to, or better than, traditional (KNN) and generative (CTGAN, TVAE) methods. These results highlight the potential of LLMs as a flexible and effective solution for clinical data imputation, capable of leveraging semantic context to capture complex relationships in medical data without requiring changes to existing analytical pipelines.