La Stampa says United may have been given a glimmer of hope in their pursuit of Ronaldo.
The Premier League giants are keen to secure the Portugal international's return to Old Trafford this summer.
And reports in Italy indicate their biggest rivals for a deal could be priced out of signing the forward.
Real want £133m (€150) for Ronaldo, who's won five Ballon d'Ors to date.
That figure may prove too high for Juventus, but not for mega-rich United.
Meanwhile, the Independent says United have lodged an enquiry with Real about re-signing the 33-year-old, who left them in 2009.
However, Real are believed to have rebuffed United's approach, partly because talks with Juventus are so advanced.