Portuguese paper A Bola claim that Ronaldo is still reluctant to discuss a new deal, having expressed his unhappiness at Real Madrid earlier this season.
Ronaldo has been linked with moves to Manchester United and Paris St Germain.
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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.