This article investigates a control system within the context of six-generation wireless networks. The control performance optimization confronts the technical challenges that arise from the intricate interactions between communication and control sub-systems, asking for a co-design. Accounting for the system dynamics, we formulate the sequential co-design decision-makings of communication and control over the discrete time horizon as a Markov decision process, for which a practical offline learning framework is proposed. Our proposed framework integrates large language models into the elements of reinforcement learning. We present a case study on the age of semantics-aware communication and control co-design to showcase the potentials from our proposed learning framework. Furthermore, we discuss the open issues remaining to make our proposed offline learning framework feasible for realworld implementations, and highlight the research directions for future explorations. Index Terms 6G, control performance optimization, communication and control co-design, Markov decision process, reinforcement learning, large language models. Wireless networked control systems (NCSs) have been focal in contemporary engineering and industrial applications, owing to the flexibility, scalability and cost-savings [1].