We investigate the identification of idiomatic expressions—a semantically non-compositional subclass of multiword expressions (MWEs)—in running text using large language models (LLMs) without any fine-tuning. Instead, we adopt a prompt-based approach and evaluate a range of prompting strategies, including zero-shot, few-shot, and chain-of-thought variants, across multiple languages, datasets, and model types. Our experiments show that, with well-crafted prompts, LLMs can perform competitively with supervised models trained on annotated data. These findings highlight the potential of prompt-based LLMs as a flexible and effective alternative for idiomatic expression identification.