Recently, the development of mobile edge computing has enabled exhilarating edge artificial intelligence (AI) with fast response and low communication cost. The location information of edge devices is essential to support the edge AI in many scenarios, like smart home, intelligent transportation systems and integrated health care. Taking advantages of deep learning intelligence, the centralized machine learning (ML)-based positioning technique has received heated attention from both academia and industry. However, some potential issues, such as location information leakage and huge data traffic, limit its application. Fortunately, a newly emerging privacy-preserving distributed ML mechanism, named federated learning (FL), is expected to alleviate these concerns. In this article, we illustrate a framework of FL-based localization system as well as the involved entities at edge networks. Moreover, the advantages of such system are elaborated. On practical implementation of it, we investigate the field-specific issues associated with system-level solutions, which are further demonstrated over a real-word database. Moreover, future challenging open problems in this field are outlined.