"Juventus is not for sale", said a source close to Exor, the holding company of the Agnelli family.
Tether, which already has an 11.5-per-cent stake in Juventus, said in a statement it "has submitted a binding all cash proposal to Exor to acquire its entire stake".
Exor has controlled Juventus since 1923, and currently has a 65.4 per cent stake in the club.
According to wire service ANSA, Tether offered 2.66 euros a share, valuing the company at 1.1 billion (£820 billion). Juventus shares closed at 2.19 euros on Friday on the Milan stock market.
Amid rumours of a possible Saudi investment, Exor had earlier Friday insisted it had no intention of selling its shares.
And the source close to Exor stressed to AFP on Friday night that this remained the case, whether to Tether or anyone else.
Tether controls USDT, a popular stablecoin - a cryptocurrency designed to hold a steady value by being pegged to traditional assets.
In the statement, its chief executive, Paolo Ardoino, said that if the deal was accepted, his company intended to invest one billion euros in the development of the club.
"Tether is in a position of strong financial health and intends to support Juventus with stable capital and a long horizon," he said.