The 24-year-old enjoyed a successful season with Los Blancos in their last campaign, as, under the guidance of Mourinho, they wrestled back the Liga title from their fierce rivals, Barcelona.
"With the coach I've grown in every way. I'm better tactically and I have more faith in the things I do. The trust he has shown in me since the first day is spectacular and I only have words of gratitude for him," the winger told Marca.
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"There is no doubt that Mourinho is a coach very special to me. With him I have improved each year and it pains me that because of injuries last season I could not give more. "
Di Maria believes that under Mourinho the team is always improving, and thinks that this helps their chance of winning more trophies.
“[With Mourinho] the team can win many more titles. Each year we spend together we continue to improve, and hopefully this year we can take another step forward. This team has no limits, but to achieve the objectives we have to work hard.
"As a team our primary target is to win the Champions League, that is what we all want and have on our minds. Personally, I dream of being one of the top 10 players in the world and we will see what happens with the Ballon d'Or."
On the initial hostile reception he received from the fans, he said: "It was difficult to win people over at the Bernabeu at first, but every match I conquered them slowly. Now I am very happy, the love I receive from people every time I step out onto the pitch is spectacular and I hope it stays that way."
Real Madrid start their Liga campaign at home to Valencia on August 19.