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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.