"Juventus, our history and our values are not for sale," said Exor CEO John Elkann, who wore a team hoodie in a rare video address posted on the Turin-based Serie A club's website.
Tether, headquartered in El Salvador and run by Italian Paolo Ardoino, a Juventus supporter, said on Friday it had submitted an all-cash proposal to buy Exor's stake in the club.
Tether said it would make a public tender offer for the remaining Juventus shares at the same price, and it planned to invest one billion euros to support the club known in Italy as Juve if the deal goes ahead.
The crypto company is offering Exor 2.66 euros per share, a source familiar with the matter said, valuing Juventus at just over one billion euros and offering a 21% premium over Juventus' closing share price of 2.19 euros.
Amsterdam-listed Exor said in a statement its board had unanimously rejected the offer and had "no intention of selling any of its shares in Juventus to a third party."
Juventus has not made an annual net profit for almost a decade, and its shares are down 27% so far this year.
Tether, the issuer of a US dollar-referenced stablecoin dubbed USDT, has already built a stake of more than 10% in Juventus this year, becoming its second-largest shareholder.
By acquiring a European club, Tether - whose business faces mounting EU regulatory scrutiny - could hope to gain credibility with the continent's establishment, while boosting its wider popularity.
Tether said it is proposing to buy Exor's 65.4% of the total Juventus share capital, without officially disclosing a price.
Exor, the largest shareholder in automaker Stellantis and which controls sports car-maker Ferrari, has been streamlining its Italian portfolio.
This year it agreed the sale of truck maker Iveco to India's Tata Motors, and said on Monday it was in talks with Greek media group Antenna to sell its news operations, including two major newspapers and three popular radio stations.
A sale of Juventus would likely be seen as the clearest sign yet of the family's gradual disengagement from their home country. The family's ties with the club date back to 1923 when Edoardo Agnelli became chair, and Elkann said in November that the family had no intention of selling shares.
Investors, led by Exor, have poured around a billion euros of fresh cash into Juventus in the past seven years.
Juventus has won the Italian championship 36 times, more than any other team, but has struggled since its ninth consecutive title in 2020. It currently sits in seventh place in Serie A.
Once home to stars such as Michel Platini, Roberto Baggio, Alessandro Del Piero and Cristiano Ronaldo, Juventus has helped the Agnellis build consensus and popularity in Italy.
Its support has weathered match-fixing and financial scandals, the most recent in 2023, when a false accounting case linked to player trading led to a 10-point deduction in Serie A.
Juventus was also a driving force behind the failed attempt to launch a breakaway European Super League with a dozen other top clubs in 2021, challenging the authority of European football's governing body UEFA.
Like other leading Serie A teams, it has had a hard time remaining competitive financially amid the growing dominance of England’s Premier League and European powerhouses such as Real Madrid, Barcelona and Paris Saint-Germain.
Tether's USDT accounts for more than half the market of stablecoins pegged to the dollar, the Bank of Italy says.
It had a market capitalisation of around $186 billion as of Friday. The token is backed by US Treasuries and dollars, and Tether is one of the 20 largest holders of US government debt.
Stablecoins are digital tokens that aim to maintain a stable value through a one-to-one peg to a traditional currency. They are backed by reserves, government bonds or deposits.