Yes Cornelius, Saruman does know that Gandalf has a ring but the thing about the three is that you couldn’t see them unless you had the One. Saruman may or may not have known this but he certainly couldn’t see it on Gandalf’s finger and he was probably caught up in the excitement of getting one of his biggest threats out of the way.
Well that explains why Frodo can see Galadriel’s ring, but does he ever see Gandalf’s? And what if Gandalf (or Galadriel) removes it to take a shower or something…how do they find it again?? 
What would Saruman have been able to do with Gandalf’s ring (Narya?) anyway? I don’t know much about what the Three could do.
The ability to make impressive fireworks might be useful, and it could come in handy should the Nazgul approach, but what else is he going to do with it? Preserve the sanctuary of what’s left of Isengard? Inspire Theoden to attack him? (or, if he does it really well, Galadriel? That would be interesting)?
You know, I don’t have RotK handy but now that you mention it, I don’t think Gandalf wore his ring. Wasn’t there a line when they were at the Grey Havens that said something like: “And they saw Gandalf’s ring, for he wore it openly now.”?
I’ll check later and come back, unless Qadgop beats me to it 
[record scratch sound]
O yes…hehe…I forgot about that little tidbit. 
Maybe it’s like emarkp said: Saruman is lying. He is pulling a ruse on Gandalf. Maybe? Huh? Maybe.
[slinks away]
What was the purpose of the dwarves’ Seven Rings? Why didn’t they turn into ringwraiths as well? If Sauron couldn’t affect them, what would the affect of the One Ring be on them?
FAQ of the rings has lots of answers to those questions.
Wow! Thanks Qadgop.
He’s Mormon too?
Get it?Donny Osmond=Joeseph…aww forget it.