However we do not know for sure, as there's no evidence to suggest that George R. R. Martin wasn't inspired by Tolkien in this particular way.
From my extensive knowledge and a search of many of his talks and posts, I can tell you that he hasn't mentioned this. This is probably because no one has asked him this question in the past1.
Now, there are certain similarities to these characters:
- Saruman uses literal birds as spies
- Varys uses little children which he calls his "little birds" as spies
- Saruman is a sorcerer of sorts
- Varys is an enigmatic character (but says he's against magic)
I think that's about where the similarities end. In fact, the point of turning the literal birds controlled by magic (in Saruman's case) into figurative ones which are real (in Varys' case) is actually a big deal. To me, this is an anti-pattern.
You see, although GRRM has said that he is very much inspired by Tolkien's writing in general; for example, he has mentioned on numerous occasions2 that his magic is "off screen" similar to in Tolkien's Lord of the Rings works. However, he tends to find faults3 in them and goes about "correcting" them, adding an even more "realistic" approach.
But wait, there's
A better question would be, is Bloodraven's Raven inspired by Saruman's Crebain?
- Gnarly old white magic dude
- Controls birds and uses them as spies
- You don't know whether he is good or bad, at first
- Plays an "overwatch" and influencer role
- Uses Ravens/Crows/Crebain to spy for him
1. If you'd like to, you can ask him directly yourself via his twitter account, @GRRMSpeaking(which he doesn't really respond to) or his Live Journal, Not a Blog (which he does seem to respond to).
2. For example in this article in So Spake Martin
3. GRRM speaks about the difference in his and Tolkien's writings, youtube