OCR of historical handwritten documents is still a challenging task and an active research field due to the relatively low recognition accuracy achieved when processing manuscripts of different writing styles. In this work, we study the use of Large Language Models (LLMs) for correcting OCR in old Greek handwritten documents. We analyze two different old Greek datasets using a Deep Network based OCR along with several well-known and easy-to-use LLMs for correcting the output. Additionally, we generate synthetic erroneous texts and modify the LLM prompts to further investigate how LLMs perform in correcting noisy old Greek text. Experimental results show the potential of LLMs for OCR correction of old Greek handwritten documents, especially in cases where the recognition results are relatively poor.