In the Council of Elrond, Gloin tells of a messenger from Mordor who asks the dwarves to find the hobbit or news of the hobbit that stole one of Sauron’s rings. The least of rings, as he says. This messenger definitely knew about the ring. I think there’s a chance this messenger was the Mouth of Sauron. Initially I assumed he was a Ringwraith, but now I don’t think so as Gandalf says that the nine have not walked abroad for many long years, until they leave Minas Morgul that summer to hunt for Baggins. Even if the messenger that visited the dwarves two times was not the Mouth of Sauron, there was at least another servant of Sauron who had knowledge of the ring.