One of the most important yet onerous tasks in the academic peer-reviewing process is composing meta-reviews, which involves understanding the core contributions, strengths, and weaknesses of a scholarly manuscript based on peer-review narratives from multiple experts and then summarizing those multiple experts' perspectives into a concise holistic overview. Given the latest major developments in generative AI, especially Large Language Models (LLMs), it is very compelling to rigorously study the utility of LLMs in generating such meta-reviews in an academic peer-review setting. In this paper, we perform a case study with three popular LLMs, i.e., GPT-3.5, LLaMA2, and PaLM2, to automatically generate meta-reviews by prompting them with different types/levels of prompts based on the recently proposed TELeR taxonomy. Finally, we perform a detailed qualitative study of the meta-reviews generated by the LLMs and summarize our findings and recommendations for prompting LLMs for this complex task.