The recent rise of Large Language Models enables novel possibilities within social robotics. Human-robot interaction and verbal communication, in particular, stand to benefit significantly from how these models generate and interpret language. Recent experiments with our social robot revealed that users expect the robot to answer general knowledge questions and recall previous activities and conversations, creating bonds and engaging interactions. This paper introduces an Episodic Memory System for social robots based on offline Large Language Models designed to store and recall past experiences. The system records relevant episodes to answer user queries about previous activities and conversations and proactively suggests personalised activities based on those the user has previously enjoyed or completed. The goal is to define personalised interactions to promote human-robot bonding and engagement as humans do. We evaluated four open-source language models, comparing them in terms of success rate to answer questions about past episodes, computational requirements, and response time. We selected these models considering the robot’s hardware limitations and computational needs. We found the well-known Meta LLaMA 3 Large Language Model the best option, providing accurate responses in reasonable response times. We then integrated the model into the Mini social robot to show the system’s performance in a human-robot interaction case study.