Conversational Recommender Systems (CRSs) aim to provide personalized recommendations by capturing user preferences through interactive dialogues. Explainability in CRSs is crucial as it enables users to understand the reasoning behind recommendations, increasing system transparency and trustworthiness. However, current CRSs often leverage knowledge graphs (KGs) or language models to extract and represent user preferences as latent vectors, which limits their explainability. Large language models (LLMs) offer powerful reasoning capabilities that can bridge this gap by generating human-understandable preference summaries. However, effectively reasoning over user preferences in CRSs remains challenging as LLMs pre-trained on large-scale corpora may not be well-suited for analyzing user preferences. While KGs provide rich domain knowledge, integrating them with LLMs encounters a significant modality gap between structured KG information and unstructured conversations. In this paper, we propose COMPASS, a plug-and-play framework that synergizes LLMs and KGs to reason over user preferences, enhancing the performance and explainability of existing CRSs. COMPASS employs a two-stage training approach: first, it bridges the gap between the structured KG and natural language through novel graph entity captioning pre-training. Next, COMPASS optimizes user preference reasoning via knowledge-aware instruction fine-tuning, where the LLM learns to reason and summarize user preferences from dialogue histories and KG-augmented context. This enables COMPASS to perform knowledge-aware reasoning and generate interpretable user preferences that can seamlessly integrate with existing CRS models for improving recommendation performance and explainability. Our experiments on benchmark datasets demonstrate the effectiveness of COMPASS in improving various CRS models.