I see and hear this over and over again, and I have not the slightest idea where it comes from.
From The Phrase Finder
Various authors over the centuries, including Shakespeare, have made reference to birds, feathered or otherwise, giving messages. The first that comes close to our current version of this phrase is Frederick Marryat, in Peter Simple, 1833:
"A little bird has whispered a secret to me."
Peter Simple is an 1834 novel written by Frederick Marryat about a young British midshipman during the Napoleonic wars. It was originally published in serialized form in 1833
Phrase Finder says that the root source of this expression probably is biblical, from Ecclesiastes; see Barrie England's answer, above.
(The phrase "feathered or otherwise" seems odd. I thought all birds, by definition, had feathers.)
The first thing that came to my mind were Odin's ravens, Thought and Memory who "brought information to Odin".
On Wiktionary, they make reference to the same Bible phrase AND a connection to Norse mythology.