Despite living in the era of the internet, phone-based scams remain one of the most prevalent forms of scams. These scams aim to exploit victims for financial gain, causing both monetary losses and psychological distress. While governments, industries, and academia have actively introduced various countermeasures, scammers also continue to evolve their tactics, making phone scams a persistent threat. To combat these increasingly sophisticated scams, detection technologies must also advance. In this work, we propose a framework for modeling scam calls and introduce an LLM-based real-time detection approach, which assesses fraudulent intent in conversations, further providing immediate warnings to users to mitigate harm. Through experiments, we evaluate the method's performance and analyze key factors influencing its effectiveness. This analysis enables us to refine the method to improve precision while exploring the trade-off between recall and timeliness, paving the way for future directions in this critical area of research.