Containing a story which is a precursor to a famous passage in her novel Jane Eyre, it was bought for £690,850 by La Musee des Lettres et Manuscrits in Paris in 2011.
It features three short stories, one of which describes a murderer driven to madness after being haunted by his victims, and how "an immense fire" burning in his head causes his bed curtains to set alight.
The museum closed amid a financial scandal and the manuscript will be auctioned in Paris next week. The Brontë Parsonage Museum in Haworth, West Yorkshire, is bidding to buy the 20-page book and return it to the literary family’s home. The miniature publication, called Young Men's Magazine Number 2, measures just 35mm x 61mm.
The Museum believes this is "a clear precursor" of a scene between Bertha and Edward Rochester in Jane Eyre, Charlotte’s classic novel, which would be published 17 years later.
The book is expected to sell for £650,000 at next Monday’s auction. A crowdfunding appeal launched by the Museum has raised £53,000, which would be added to funds pledged from other institutions for the bid.
Dame Judi, president of the Brontë Society, said: “These tiny manuscripts are like a magical doorway into the imaginary worlds they (the sisters) inhabited and also hint at their ambition to become published authors.”
The book has been in private hands since Charlotte's death in 1855 at the age of 38.
The Museum said: “It came up for auction once before, just eight years ago, only to slip through our grasp and disappear into a private collection. It has barely been seen since.”
Charlotte carefully folded and stitched the little magazine into its brown paper cover and filled it with over 4,000 tiny written words.
It is one in a sequence of six little books, of which five are known to have survived. Four are currently housed at the Yorkshire museum.