Marca in Spain and A Bola in Portugal led their Tuesday print editions by amplifying a claim made on Spanish TV station La Sexta's "Jugones" show on Monday night that Real Madrid had agreed to sell Ronaldo to Juventus for €100 million.
Ronaldo won his fifth Champions League title with Madrid in May.
The Portugal superstar spoke about the club in the past tense after that game when he said: "We will talk in the future".
ESPN Deportes' Paola Nunez reported that the "Jugones" story means that Real Madrid are at least considering the possibility of negotiations with Juventus.
Speculation has mounted that Juve may make a bid of £88m for Ronaldo, who has hinted that he could leave Real.
While Ronaldo's World Cup dream ended last week with defeat to Uruguay in the last-16, Matuidi is preparing for France's quarter-final tie with the South Americans on Friday (3pm).
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"I would prefer if they go for Mbappe as he would be a long-term investment because he is six years younger and is already at the top level".
Despite the glut of silverware, however, the five-time world player of the year has had frequent fallouts with Real and has declared on several occasions over the years that he wants to leave the club.
"I think Madrid have interest in him, but I do not know about any offers or any potential bids, but it would be almost impossible to sign a player who can sell a lot like him. I'll give a response in the coming days".
"However, today I'm a player of the French national team and we have bigger fish to fry, no?"
A win over Uruguay would book France a semi-final clash with either Brazil or Belgium, and were they to be successful, they would face one of England, Sweden, Croatia or Russian Federation in the final.