The BBC said Clarkson submitted the top bid of $230,000 to buy the turquoise and gold ring -- one of only three items of jewelry known to have belonged Austen -- at an auction last year.
However, Minister for Culture, Communications and Creative Industries Ed Vaizey has put a temporary export bar on the ring and appealed to U.K. buyers to come forward in an attempt for the "national treasure" to be "saved for the nation."
Buyers have until Sept. 30 to match the amount Clarkson has pledged for the ring and if no one does so the "American Idol" winner will be allowed to take it home.
"Jane Austen's modest lifestyle and her early death mean that objects associated with her of any kind are extremely rare, so I hope that a U.K. buyer comes forward so this simple but elegant ring can be saved for the nation," Vaizey told the BBC.
Austen was the author of the classic 19th century novels "Pride and Prejudice," "Sense and Sensibility" and "Emma."