The Argentina international is desperate for success ahead of the new season, and is confident they can get the ball rolling by beating Barcelona in the Supercopa
After winning the Copa del Rey in 2010-11 and La Liga last term, the Argentine winger believes the Blancos must approach the new campaign with high expectations, and be ready to challenge on all fronts.
"Will this be our year in the Champions League? I hope so, but let's hope that it's not only the year we win the Champions League," Di Maria was quoted as saying by the club's official website.
"Right from the start we're conscious that we're out to win everything and that we're going to fight to win all the titles, which is what Real Madrid must do year after year.
Di Maria then looked ahead to the Supercopa against Barcelona in under two weeks time, and is confident Madrid have what it takes to beat their arch-rivals.
"Last year we faced them pn various occasions and we know that we have all the chances in the world to beat them," he added.
"In addition, it's all going to happen in our first match back at the Santiago Bernabeu, and that's very important for us."
The first leg of the annual Spanish curtain raiser takes place at Camp Nou on August 23.