The hand-stitched volume, measuring less than two-and-a-half inches, is to be auctioned in Paris on Monday afternoon, and is expected to fetch at least £650,000.
The museum at the Brontë family’s parsonage home at Haworth hopes to return it there, to sit alongside others written by Charlotte.
It has been applying to charitable trusts to raise the funds, and hopes to secure the final £80,000 though its online appeal.
“We’re currently at 626 donors, pledging gifts totalling almost £58,000,” aid a spokesman at the museum. “We will be continuing to accept donations up until 11am on Monday.”
The TV dramatist Sally Wainwright, whose film about the Brontë sisters, To Walk Invisible, was filmed partly at Haworth, said Charlotte’s little book belonged there.
“A shy, brilliant 14-year-old girl wrote this book in Yorkshire in 1830, with very little idea that one day she would be a global literary superstar,” Ms Wainwright said.
“We have to bring this book back to Yorkshire, where it was written, where it belongs.”
The poet laureate, Yokshire-born Simon Armitage, has promised a bottle of Laureate’s Choice sherry, a traditional perk of his honorary title, to the donor who takes the total past £80,000.