Gazzetta dello Sport claim that talks are underway on an 100 million euro deal for the Portuguese star.
Ronaldo has the same agent as Jose Mourinho, and the reports suggest he could follow the forward to Paris.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.