The newspaper said its story was based on a reliable source and that the 32-year-old four-times world player of the year had already made up his mind to ask the club for a transfer.
It said that Ronaldo was "deeply disenchanted" with the allegations against him.
Record, another sports daily, carried a similar story.
Ronaldo's agents could not immediately be reached for comment.
Spanish prosecutors have filed a lawsuit against the player accusing him of defrauding tax authorities of 14.7 million euros ($16.5 million) by hiding his image rights income between 2011 and 2014. Ronaldo has denied any wrongdoing.
Real Madrid said on Thursday they were confident the Portuguese forward had acted legally. They could not immediately be reached on Friday to comment on the report.
Ronaldo led Real Madrid to their 12th European Cup earlier this month after scoring two goals in a 4-1 victory over Juventus in the Champions League final, becoming the tournament's top scorer.
Ronaldo, Portugal's all-time leading scorer, is the latest in a long line of soccer players in Spain -- among them Barcelona's Lionel Messi and Neymar -- to be caught up in cases over tax or transfers.
Ronaldo has completed eight seasons at Real Madrid since joining them from Manchester United in 2009 for a then world record fee of 96 million euros
During that time, they have won the Champions League three times and La Liga twice. In November, he agreed to extend his contract until 2021.
He is currently at the Confederations Cup in Russia with the Portuguese national team where his team mate Andre Silva said that Ronaldo was motivated for the tournament.
"All I can say is that he is motivated, focused on the national team and encouraging us on to win the tournament," he told a news conference in Kazan, where Portugal face Mexico on Sunday.
(Writing by Brian Homewood in Berne; Editing by John O'Brien and Edmund Blair)
