In recent years, Large Language Models (LLMs) have shown great abilities in various tasks, including question answering, arithmetic problem solving, and poem writing, among others. Although research on LLM-as-an-agent has shown that LLM can be applied to Reinforcement Learning (RL) and achieve decent results, the extension of LLM-based RL to Multi-Agent System (MAS) is not trivial, as many aspects, such as coordination and communication between agents, are not considered in the RL frameworks of a single agent. To inspire more research on LLM-based MARL, in this letter, we survey the existing LLM-based single-agent and multi-agent RL frameworks and provide potential research directions for future research. In particular, we focus on the cooperative tasks of multiple agents with a common goal and communication among them. We also consider human-in/on-the-loop scenarios enabled by the language component in the framework.