The Daily Star reports that Ronaldo has told Real Madrid president Florentino Perez that he is unhappy at the club and wants to leave.
City are reportedly prepared to offer the 27-year-old a massive four-year contract.
The former Manchester United star is currently being paid around £250,000 a week in Madrid.
Sources close to the player told the Daily Star: “This is a situation that has been brewing for a long time.”
Ronaldo reportedly has a €1bn buy-out clause in his contract.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.