The text 'a little bird told me' doesn't appear in any version of the Bible. The root source of this expression is probably biblical though, from Ecclesiastes 10-20 (King James Version):
"Curse not the king, no not in thy thought; and curse not the rich in thy bedchamber: for a bird of the air shall carry the voice, and that which hath wings shall tell the matter."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."
A source one cannot or will not identify gave this information, as in How did you learn they were getting a divorce?--Oh, a little bird told me. Versions of this idiom date from ancient times and appear in numerous proverb collections.