I know that it is definitely stated that he did not know that Gandalf had a ring (that Cirdan had secretly given it to him upon his arrival to Middle Earth), but I always thought that he would have known that Elrond and Galadriel had the other rings and probably presumed that Cirdan still had the other.
The whole purpose of the White Council was to discuss and keep watch upon the rings of power. Saruman, being on the council and not even evil at first, would have been in the loop about who had what for the most part.
Correct me if I'm wrong, but I don't think I am.
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Those who the Gods would destroy, They first make mad.
~Those Crazy Greeks
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