The Argentine star, who became Manchester United's record signing in the summer when he joined the club for just under £60m, made the comment in a lengthy interview in the Daily Mail.
"Rooney is at the top level," said Di Maria.
"The other day I was talking to my friend and I said, 'Rooney and me understand each other, just like Messi and me in the Argentina squad, or Cristiano at Real Madrid.'
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"I get on really well with Rooney, we get together on the pitch to kick the ball about, to do things.
"He’s a spectacular player and he’s one of the top players in the game."
Di Maria, who has recorded more assists (20) than any other player in Europe in 2014, added that it is "a pleasure and a point of pride" to star alongside Rooney - and admits that, back when he was a teenager, he used to watch and admire the England striker.
The 26-year-old also spoke about how he is not too worried missing out on Champions League football - and how he hasn't even watched the competition on television this season.
"I play with my daughter instead," he said. "It’s more important.
"So, no, I don’t worry about the Champions League. I knew when I came to Manchester that I wouldn’t be playing in the Champions League but what I was thinking — what I think now —was that I would do my bit to help my team-mates qualify for the Champions League so that the next year we would be back playing important games.
"I think that will happen."
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