The draft was noticed be missing by Penguin Random House according to laywers acting on behalf of the publisher.
A spokeswoman for Penguin Random House said: "Grey will be published on June 18 - Christian Grey's birthday - as planned. We have no further comment to make due to the ongoing police investigation."
James said she wrote the book after huge demand from fans. On the opening page, she says it is "dedicated to those readers who asked ... and asked ... and asked ... and asked for this".
The first of the trilogy of the books, which has sold more than 125 million copies worldwide, was turned into a hit film which starred Holywood-born actor Jamie Dornan as the lead title and Dakota Johnson.
The Fifty Shades trilogy - Fifty Shades Of Grey, Fifty Shades Darker and Fifty Shades Freed - has sold more than 125 million copies around the world.
It has made James a millionaire many times over. This year's Sunday Times Rich List estimated her fortune at £75 million.
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