Well, Gandalf did say "in" not "on," so Wormtongue might not quite know what he was talking about.
But I doubt there was much question in Saruman's mind as to where the Three might be. As I recall, there's a statement, possibly in the Silmarillion (don't have the books on hand to check) that says the Wise (in whose numbers Saruman was counted) discerned before the end of the Third Age that one was with Elrond in Rivendell, another with Galadriel in Lorien, and the third possibly with Cirdan at the Havens. As the head of the White Council, Saruman would likely have had plenty of opportunity to figure this out. Saruman also had discerned that Gandalf had the third, likely before he became enmeshed with Sauron, as it was one of the roots of his jealousy toward Gandalf. So no surprise there. By the time Gandalf sang his little ditty (for which I also wrote a tune maybe 30 years ago), Saruman doubtless had a clear idea where the Three were located, but whether or not Sauron got that information from him... I wonder. I know Sauron attacked Lothlorien more than once, so he might have suspected a Ring was there, but I can't recall if there were similar attacks on Rivendell (I know, I should bestir myself to go upstairs and check the books, but it's almost nap time
).