As Large Language Models (LLMs) are increasingly being employed in real-world applications in critical domains such as healthcare, it is important to ensure that the Chain-of-Thought (CoT) reasoning generated by these models faithfully captures their underlying behavior. While LLMs are known to generate CoT reasoning that is appealing to humans, prior studies have shown that these explanations do not accurately reflect the actual behavior of the underlying LLMs. In this work, we explore the promise of three broad approaches commonly employed to steer the behavior of LLMs to enhance the faithfulness of the CoT reasoning generated by LLMs: in-context learning, fine-tuning, and activation editing. Specifically, we introduce novel strategies for in-context learning, fine-tuning, and activation editing aimed at improving the faithfulness of the CoT reasoning. Our empirical analyses on multiple benchmarks indicate that these strategies offer limited success in improving the faithfulness of the CoT reasoning, with only slight performance enhancements in controlled scenarios. In summary, our work underscores the inherent difficulty in eliciting faithful CoT reasoning from LLMs, suggesting that the current array of approaches may not be sufficient to address this complex challenge.