With 5G cellular systems being actively deployed worldwide, the research community has started to explore novel technological advances for the subsequent generation, i.e., 6G. It is commonly believed that 6G will be built on a new vision of ubiquitous AI, an hyper-flexible architecture that brings human-like intelligence into every aspect of networking systems. Despite its great promise, there are several novel challenges expected to arise in ubiquitous AI-based 6G. Although numerous attempts have been made to apply AI to wireless networks, these attempts have not yet seen any large-scale implementation in practical systems. One of the key challenges is the difficulty to implement distributed AI across a massive number of heterogeneous devices. Federated learning (FL) is an emerging distributed AI solution that enables data-driven AI solutions in heterogeneous and potentially massive-scale networks. Although it still in an early stage of development, FL-inspired architecture has been recognized as one of the most promising solutions to fulfill ubiquitous AI in 6G. In this article, we identify the requirements that will drive convergence between 6G and AI. We propose an FL-based network architecture and discuss its potential for addressing some of the novel challenges expected in 6G. Future trends and key research problems for FL-enabled 6G are also discussed.