The recent success of large language models (LLMs) has spurred their application in various fields. In particular, there have been efforts to integrate LLMs into various aspects of wireless communication systems. The use of LLMs in wireless communication systems has the potential to realize artificial general intelligence (AGI)-enabled wireless networks. In this paper, we investigate an LLM-based resource allocation scheme for wireless communication systems. Specifically, we formulate a simple resource allocation problem involving two transmit pairs and develop an LLM-based resource allocation approach that aims to maximize either energy efficiency or spectral efficiency. Additionally, we consider the joint use of low-complexity resource allocation techniques to compensate for the reliability shortcomings of the LLM-based scheme. After confirming the applicability and feasibility of LLM-based resource allocation, we address several key technical challenges that remain in applying LLMs in practice.