Speculative decoding has emerged as a promising approach to accelerating large language model (LLM) generation using a fast drafter while maintaining alignment with the target model's distribution. However, existing approaches face a trade-off: external drafters offer flexibility but can suffer from slower drafting, while self-speculation methods use drafters tailored to the target model but require re-training. In this paper, we introduce novel drafters based on Mamba, a state-of-the-art state space model (SSM), as a solution that combines the best aspects of both approaches. By leveraging the linear structure of SSMs, our approach avoids the quadratic complexity inherent in traditional Transformer-based methods, enabling faster drafting and lower memory usage while maintaining the flexibility to work across different target models. We further enhance efficiency with a novel test-time tree search algorithm for generating high-quality draft candidates. Our empirical evaluation demonstrates that Mamba-based drafters not only outperform existing external drafting methods but are also comparable to state-of-the-art self-speculation approaches while using less memory and maintaining their cross-model adaptability.