The claim matching (CM) task can benefit an automated fact-checking pipeline by putting together claims that can be resolved with the same fact-check. In this work, we are the first to explore zero-shot and few-shot learning approaches to the task. We consider CM as a binary classification task and experiment with a set of instruction-following large language models (GPT-3.5-turbo, Gemini-1.5-flash, Mistral-7B-Instruct, and Llama-3-8B-Instruct), investigating prompt templates. We introduce a new CM dataset, ClaimMatch, which will be released upon acceptance. We put LLMs to the test in the CM task and find that it can be tackled by leveraging more mature yet similar tasks such as natural language inference or paraphrase detection. We also propose a pipeline for CM, which we evaluate on texts of different lengths.