Ronaldo, reports Don Balon, has spoken enthusiastically about Alli to Real coach Zinedine Zidane.
The England international impressed Ronaldo with his two goals in Tottenham's famous Champions League win over Real at Wembley.
And the Portuguese believes the 21 year-old would be a natural successor for Luka Modric. The Croatian, now 32, has battled for consistency this season and was outshone by Alli at Wembley.
Ronaldo has told Zidane he'd welcome Alli's arrival and believes Real should make him a priority for the 2018 market.
However, the coach believes they're overloaded in midfield as it is and his immediate plans are to strengthen other areas.