The classic tale is so popular that bookmakers are refusing to take any more bets on it winning.
But the BBC - which is behind the poll called The Big Read - says the competition is "far from over".
A shortlist of 21 books has been announced. Harry Potter And The Goblet Of Fire is also on it. The winner will be revealed on 13 December.
Other kids' books to make it to the final include Winnie The Pooh and His Dark Materials.
They are competing against classic tales including Great Expectations, Wuthering Heights and Little Women.
In the weeks leading up to the winner being announced, programmes where celebrities argue their case for their fave book are being screened.
"We would urge viewers to vote for their favourite and make a difference," said a BBC spokesman.