A German man who in 1991 discovered the 5,300-year-old iceman, Oetzi, in the Alps is now demanding up to $250,000 as a finder's reward.
Bones of contention: How much is Oetzi worth?
The provincial government of Bolzano in northern Italy, where Oetzi is a star tourist attraction, says it is considering its response.
The iceman was found in the Oetztal valley on the Austrian-Italian border by Helmut Simon and his wife Erika.
At first the couple thought it was a mountaineer who had had an accident.
It turned out to be an ancient mummy.
But while Oetzi was feted by the provincial government in Bolzano, who built a special museum for him, the Simons felt they were unfairly treated.
After several years of court proceedings, Helmut Simon was recently recognised as Oetzi's official discoverer - a move which opens up the possibility of a finder's fee.
His lawyer Elohim Rudolph Ramirez says the reward should be between $150,000 and $250,000.
"We think that it is an honest fee. The province of Bolzano makes big business with this mummy," the lawyer said.
"From the historical aspect you can't value this because it is so extraordinary - a man, a totally intact man, 5,000 years old. Mr Simon doesn't want an astronomical fee for that."
A few years ago the province of Bolzano offered Helmut Simon around $5,000 as a finder's fee. It has yet to respond to the current request.
Stefan Beikircher, a legal adviser to the province, says: "The government has always shown a readiness to offer something to Mr Simon. It's just that so many unrealistic numbers have been thrown around."
At the South Tyrol Museum of Archaeology, Oetzi lies in a newly improved refrigerated cell - oblivious to the legal rows.
The pathologist in charge of preserving him, Egarter Vigl, feels the ancient iceman should be treated with more respect.
"We have a human body and in my personal view it's not important if this man died yesterday or five thousand years ago. He is a human being, and he has to be treated as a human being and not as an object."