The query processing in distributed database management systems (DBMS) faces more challenges, such as more operators, and more factors in cost models and meta-data, than that in a single-node DMBS, in which query optimization is already an NP-hard problem. Learned query optimizers (mainly in the single-node DBMS) receive attention due to its capability to capture data distributions and flexible ways to avoid hard-craft rules in refinement and adaptation to new hardware. In this paper, we focus on extensions of learned query optimizers to distributed DBMSs. Specifically, we propose one possible but general architecture of the learned query optimizer in the distributed context and highlight differences from the learned optimizer in the single-node ones. In addition, we discuss the challenges and possible solutions.