Mobile Edge Computing (MEC) environments present significant challenges for edge server selection due to user mobility, varying network conditions, and diverse service intents. Traditional static Quality of Service (QoS)-based methods often fail to adapt to these dynamic, context-sensitive scenarios. The objective of this paper is to improve server selection quality by incorporating user intent and predicted future conditions into the decision-making process. To this end, we propose an LLM-driven multi-agent recommendation framework. The system is composed of agents responsible for user context interpretation, mobility prediction, QoS estimation, and final server selection, coordinated through a central controller. A Large Language Model (LLM) is used to infer the relative importance of QoS metrics—such as response time, throughput, server load, and failure rate—from natural language preferences, and to reason about optimal server choices. Experimental results demonstrate that our method significantly outperforms baseline approaches in server selection accuracy. The LLM successfully identifies user-prioritized QoS dimensions even from minimal input and enhances decision quality through contextual reasoning. These findings suggest that LLMs offer a promising approach to enabling adaptive, personalized, and explainable edge server recommendations in future MEC systems.