In the aftermath of Real's third successive European title in Kiev, Ronaldo said: "It was very nice to be at Real Madrid".
United's executive vice chairman Ed Woodward has long-dreamed of luring the five-time Ballon d'Or victor back to Old Trafford.
No new contract for Ronaldo?
Despite having a deal until 2021, Ronaldo remains angry and distant with his club though, aware of their stance on an improved contract.
On June 2, Corriere dello Sport reported that Ronaldo planned to stay on if he is paid 80 million euros ($94.4 million) a year, and has hinted that he could leave Real following the team's Champions League win.
At the moment there is no offer for Ronaldo and Madrid are not looking for one either.
Paris Saint-Germain, Manchester United, Bayern Munich, and Juventus are interested in acquiring the captain of the Portuguese national squad.
Despite not scoring a goal, the Real star's return to the side following a brief break after the Champions League final, inspired them to end a two-match winless streak.