Earlier this month, the British government placed a temporary export ban on the gold-and-turquoise ring in the hope that money could be found to keep it in Britain.
The Jane Austen's House museum said it had raised 103,200 pounds of the 152,450-pound asking price since launching a fundraising campaign on Friday, most of it from a single anonymous donation.
"We are two-thirds of the way there in 48 hours, which is tremendous, but we're not there yet," said museum fundraiser Louise West.
The museum at Austen's former home in Chawton, southern England, had hoped to buy the ring last year but was outbid when it sold for five times the estimated price.
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Clarkson an Austen fan who owns a first edition of the author's novel "Persuasion" - was the successful buyer. But she has been prevented from taking the ring home to the US by a power that allows the British government to temporarily halt the export of works judged to be national treasures.
West said the situation is a shame for Clarkson, "but the ring should stay in this country, because there is so little of Austen's personal effects left."
West said the museum had invited the 2002 "American Idol" winner to come visit the next time she is in Britain. She said Clarkson's interest in the author was another sign that Austen's popularity remains strong, 200 years after she published her most famous novel, "Pride and Prejudice."