[Legolas]

Even Sauron knows them not. They are older than he.

This is not referring to wordly age, but rather age in terms of being under the dominion of Morgoth's evil - The Silmarillion speaks of wild 'beasts' that Morgoth let run free through Middle-earth. This might be what he's talking about.

These wild beasts are also mentioned in the description of Oromë:

He is a hunter of monsters and fell beasts,

Morgoth's beasts:

Green things fell sick and rotted, and rivers were choked with weeds and slime, and fens were made, rank and poisonous, the breeding place of flies; and forests grew dark and perilous, the haunts of fear; and beasts became monsters of horn and ivory and dyed the earth with blood.

And Oromë tamer of beasts would ride too at whiles in the darkness of the unlit forests; as a mighty hunter he came with spear and bow, pursuing to the death the monsters and fell creatures of the kingdom of Melkor, and his white horse Nahar shone like silver in the shadows.

There countless became the hosts of his beasts and his demons, and the race of the Orcs, bred long before, grew and multiplied in the bowels of the earth.

But as the third age of the captivity of Melkor drew on, the Dwarves became troubled, and they spoke to King Thingol, saying that the Valar had not rooted out utterly the evils of the North, and now the remnant, having long multiplied in the dark, were coming forth once more and roaming far and wide. 'There are fell beasts,' they said, 'in the land east of the mountains, and your ancient kindred that dwell there are flying from the plains to the hills.'

Now these were a woodland people (the Nandor) and had no weapons of steel, and the coming of the fell beasts of the North filled them with great fear, as the Naugrim declared to King Thingol in Menegroth.

etc.