Di Maria spent four years at Real Madrid with Ronaldo before his move to Old Trafford at the start of this season, while Messi is a long-time team-mate with Argentina.
The goalscoring exploits of Ronaldo and Messi continue to amaze all onlookers, as the duo underline their status as the greatest two players on the planet.
Since the inception of the FIFA Ballon d'Or in 2010, the pair have picked up the award on every occasion, Messi clinching the title in its first three years before Ronaldo laid claim to it in 2013 and 2014.
Ronaldo also won the FIFA World Player of the Year gong in 2008, with Messi taking the honours 12 months later.
The pair have constantly been compared - something which Di Maria insists is a futile task - and the Manchester United man believes their dominance merits a special prize.
"I always say the same thing: that they're two completely different players," he told FIFA.com.
"Leo features in every game, making short bursts and nonchalantly dribbling past one, two or three players with great ball control in tight spaces.
"Cristiano is more about power, long range shots... they're different.
"If I were FIFA, I'd have two Ballon d'Or prizes, one for that pair to fight over, and another for everyone else."
