Large Language Models (LLMs), with their abilities in knowledge acquisition and reasoning, can potentially enhance the various aspects of Self-adaptive Systems (SAS). Yet, the potential of LLMs in SAS remains largely unexplored and ambiguous, due to the lack of literature from flagship conferences or journals in the field, such as SEAMS and TAAS. The interdisciplinary nature of SAS suggests that drawing and integrating ideas from related fields, such as software engineering and autonomous agents, could unveil innovative research directions for LLMs within SAS. To this end, this paper reports the results of a literature review of studies in relevant fields, summarizes and classifies the studies relevant to SAS, and outlines their potential to specific aspects of SAS.