The growth of Massive Open Online Courses (MOOCs) presents significant challenges for personalized learning, where concept recommendation is crucial. Existing approaches typically rely on heterogeneous information networks or knowledge graphs to capture conceptual relationships, combined with knowledge tracing models to assess learners' cognitive states. However, these methods face significant limitations due to their dependence on high-quality structured knowledge graphs, which are often scarce in real-world educational scenarios. To address this fundamental challenge, this paper proposes CLLMRec, a novel framework that leverages Large Language Models through two synergistic technical pillars: Semantic Alignment and Prerequisite Knowledge Distillation. The Semantic Alignment component constructs a unified representation space by encoding unstructured textual descriptions of learners and concepts. The Prerequisite Knowledge Distillation paradigm employs a teacher-student architecture, where a large teacher LLM (implemented as the Prior Knowledge Aware Component) extracts conceptual prerequisite relationships from its internalized world knowledge and distills them into soft labels to train an efficient student ranker. Building upon these foundations, our framework incorporates a fine-ranking mechanism that explicitly models learners' real-time cognitive states through deep knowledge tracing, ensuring recommendations are both structurally sound and cognitively appropriate. Extensive experiments on two real-world MOOC datasets demonstrate that CLLMRec significantly outperforms existing baseline methods across multiple evaluation metrics, validating its effectiveness in generating truly cognitive-aware and personalized concept recommendations without relying on explicit structural priors.