Recent advances in Artificial Intelligence (AI) and the Internet of Things (IoT) have facilitated continuous improvement in smart city based applications such as smart healthcare, transportation, and environmental management. Digital Twin (DT) is an AI-based virtual replica of the real-world physical entity. DTs have been successfully adopted in manufacturing and industrial sectors, they are however still at the early stage in smart city based applications. The major reason for this lag is the lack of trust and privacy issues in sharing sensitive data. Federated Learning (FL) is a technology that could be integrated along with DT to ensure privacy preservation and trustworthiness. This paper focuses on the integration of these two promising technologies for adoption in real-time and life-critical scenarios, as well as for ease of governance in smart city based applications. We present an extensive survey on the various smart city based applications of FL models in DTs. Based on the study, some prominent challenges and future directions are presented for better FL–DT integration in future applications.