They also say there is a missing line of text on the first page between the words "burnt" and "so much".
Very rare
They claim it's one of only 10,000 copies like that, as the printers stopped the presses to correct the mistake.
The book is apparently unread, and has been kept in an airtight box since it was bought in 2000 for £600.
A signed first edition of Goblet of Fire sold in 2003 for £27,500.
One Potter expert told Newsround he would be surprised if the book reached £20,000.
He thought the book was probably worth closer to £2,000.
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