While most existing dialogue studies focus on dyadic (one-on-one) interactions, research on multi-party dialogues has gained increasing importance. One key challenge in multi-party dialogues is identifying and interpreting the relationships between participants. This study focuses on multi-party chat corpus and aims to estimate participant pairs with specific relationships, such as family and acquaintances. We evaluated the performance of large language models (LLMs) in estimating these relationships, comparing them with a logistic regression model that uses interpretable textual features, including the number of turns and the frequency of honorific expressions. The results show that even advanced LLMs struggle with social relationship estimation, performing worse than a simple heuristic-based approach. This finding highlights the need for further improvement in enabling LLMs to naturally capture social relationships in multi-party dialogues.