Prerequisite skills - foundational competencies required before mastering more advanced concepts - are important for supporting effective learning, assessment, and skill-gap analysis. Traditionally curated by domain experts, these relationships are costly to maintain and difficult to scale. This paper investigates whether large language models (LLMs) can predict prerequisite skills in a zero-shot setting, using only natural language descriptions and without task-specific fine-tuning. We introduce ESCO-PrereqSkill, a benchmark dataset constructed from the ESCO taxonomy, comprising 3,196 skills and their expert-defined prerequisite links. Using a standardized prompting strategy, we evaluate 13 state-of-the-art LLMs, including GPT-4, Claude 3, Gemini, LLaMA 4, Qwen2, and DeepSeek, across semantic similarity, BERTScore, and inference latency. Our results show that models such as LLaMA4-Maverick, Claude-3-7-Sonnet, and Qwen2-72B generate predictions that closely align with expert ground truth, demonstrating strong semantic reasoning without supervision. These findings highlight the potential of LLMs to support scalable prerequisite skill modeling for applications in personalized learning, intelligent tutoring, and skill-based recommender systems.