Assigning pull requests to appropriate code reviewers can accelerate the review process and help uncover potential bugs. However, the inherent complexities in pull requests and code reviewers present challenges in making suitable matches between them. Prior studies focus on mining rich semantic information from pull requests or profile information from code reviewers to improve efficiency. These approaches often overlook the intrinsic relationships between pull requests and code reviewers, which can be represented by a combination of multiple factors and strategies, resulting in suboptimal recommendation accuracy. To address this issue, we propose CoRe, a collaborative agent-based code reviewer recommendation approach that emphasizes flexibility and adaptability. We leverage Large Language Models (LLMs) to precisely capture the rich textual semantics of both pull requests and reviewers. Additionally, we integrate various factors into the recommendation process through the robust planning, collaboration, and decision-making capabilities of multi-agent systems. This integration significantly enhances the performance of LLM-based code reviewer recommendations. We evaluate the effectiveness of our approach on four widely used projects. The results demonstrate that CoRe outperforms state-of-the-art methods in both performance and interpretability.