Tuttosport says Cambiaso, 24, is Real Madrid's backup plan in the event they fail to reach agreement for Liverpool fullback Trent Alexander-Arnold.
The Italy international is flattered, but is set to stay at Juventus .
"Just being connected with a club like Real Madrid feels like something bigger than me. I am proud of the admirers I can have: it is motivating to know that someone appreciates you, but I have not received a proposal. In any case, Juventus is my Real Madrid," he told Corriere dello Sport.
"I have extended until 2029 and I want to stay as long as possible."
The 24-year-old hopes Juventus can challenge for the league title this season.
"We deserve the top spots and Juventus always play to win," he says. "Inter are favourites, and we can face them in two weeks. Before that we have Lazio and Stuttgart, two very high mountains. We are among the best."