The 28-year-old winger, who recently sealed a British transfer fee record switch to the Premier League outfit, has admitted he was close to joining the Red Devils ahead of the 2013/14 campaign.
He ultimately stayed and fought for his place at the Bernabeu following the purchase of Gareth Bale from Tottenham for a world record transfer fee.
And, it appears that Ronaldo played a crucial role in the talented winger sticking it out for another year in the Spanish capital.
Di Maria told ESPN Radio: “The truth is that I have a great relationship with Cristiano Ronaldo and I stayed at Madrid last season thanks to him.
“I left Madrid in the best possible way, by winning La Decima [10th European Cup crown]. In my farewell letter, I said exactly how I felt from the first day at the Bernabeu.
“I am grateful to Manchester United for meeting Madrid’s demands. But I don’t feel any extra pressure because I’m the most expensive player in the Premier League.
“The Premier League is more physical and about strength, whereas Spain was more about football. It’s a very strong league, though. Van Gaal has told me to try to adapt as quickly as possible.”