From A Wiki of Ice and Fire
Balerion is a black cat with a torn ear. As a kitten, he was owned by Rhaenys Targaryen, who liked to pretend he was the dragon Balerion. After her death, the whereabouts of the cat are unknown, though many readers believe he is the vicious one-eyed cat Arya Stark chases in A Game of Thrones and who pesters Tommen Baratheon and his kittens in A Dance with Dragons and who has been known to attack ravens in the rookery.
|“||That’s the real king of this castle right there … Older than sin and twice as mean. One time, the king was feasting the queen’s father, and that black bastard hopped up on the table and snatched a roast quail right out of Lord Tywin’s fingers. Robert laughed so hard he like to burst. You stay away from that one, child.||”|