Here is what the Sirens actually sing to Odysseus in bk. 12 of the Odyssey (Butler's translation from the Perseus website):
"‘Come here,’ they sang, ‘renowned Odysseus, honor to the Achaean name, and listen to our two voices. No one ever sailed past us without staying to hear the enchanting sweetness of our song - and he who listens will go on his way not only charmed, but wiser, for we know all the ills that the gods laid upon the Argives and Trojans before Troy, and can tell you everything that is going to happen over the whole world.’"
Isn't it interesting that they basically claim to be able to sing the Iliad and the Odyssey, and, one supposes, also The Little Ilaid and the Nostoi?
Is it really almost 30 years ago when I missed this on first reading?