I'm fairly certain that it's to be found in JRRT's writings. I didn't find it in the FotR chapter "
Council of Elrond", nor in the "Unfinished
Tales" section "The Hunt for
the Ring". Ah, found it in the FotR chapter "The Shadow of the Past". After
Gollum had left the
Misty Mountains, and followed
Bilbo's trail as far as
Esgaroth and
Dale, he returned from there, going through
Mirkwood east to west: "The Woodmen said that there was some new terror abroad, a ghost that drank blood. It climbed
trees to find nests; it crept into holes to find
the young;
it slipped through windows to find cradles."