Ronaldo's agent, Jorge Mendes, has presented the offer to Real Madrid president Florentino Perez, who must now decide whether to accept or reject it, per El Chiringuito (h/t Football Italia).
Real Madrid are said to have a "gentleman's agreement" with Ronaldo that he can leave for €100 million (£88.6 million) as long as he does not join a direct rival, per Football Italia.
Ronaldo's future at the Santiago Bernabeu has been uncertain since he helped the club win a third consecutive UEFA Champions League title in May. After the match, he said "it was beautiful to be at Real Madrid", per BelN Sports (h/t BBC Sport).
It's not the first time Ronaldo has been linked with a move away from Real Madrid, and it's often seen as a sign that the 33-year-old is after an improved contract.
However, this time there appears to be more substance to the rumours. Ronaldo has reportedly held talks with Juventus manager Massimiliano Allegri over a move, per Cadena Cope (h/t the Mirror's Liam Prenderville).
Juventus shirts bearing his name have been spotted on sale in Turin:
Mendes has also given his view on the potential transfer, per Record (h/t TalkSport).
"If this happens it will simply be a new stage, a new challenge in his brilliant career," he said. "If Cristiano Ronaldo leaves Real Madrid, he will be eternally grateful to the club, the president, all the directors, the medical staff, all the staff without exception, as well as all the Madrid fans around the world."
One potential stumbling block would be the huge fees involved in such a deal. Juventus would have to find a way of affording not just his transfer fee but his wages. The Serie A side are said to be willing to offer him a four-year deal worth €60 million (£53.1 million) a year after tax, per Goal's Robin Bairner.
Despite the fact Ronaldo is heading towards the end of his career, he has shown few signs of slowing down. He scored 41 goals for Real Madrid last season and followed that up with four goals for Portugal at the 2018 FIFA World Cup.
Juventus fans have seen firsthand just how effective Ronaldo still is. He scored a brilliant overhead kick at the Juventus Stadium in April as Real Madrid won 3-0 on their way to knocking the Italian champions out of the Champions League.
Whether they will get to watch Ronaldo in a Juventus shirt next season still remains to be seen. There's a sense that if the forward is to leave Real Madrid, it may well be this summer. However, there would also be little surprise if he opted to stay put despite all the speculation over his future.