The La Liga champions have been drawn against their English counterparts in this year's Champions League and the United shot-stopper believes they should be worried
The former Atletico Madrid man is better placed than most to give a verdict on the respective qualities of the English and Spanish champions, and he believes that Jose Mourinho's men will have to be on top of their game to match United's Manchester rivals.
"City are a great team," he told Marca. "They are full of great players in all positions. The substitutes are also top-class.
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"It will be really difficult for Real Madrid, both in the Bernabeu and in Manchester. You don't get anything for free in the Champions League."
The Spain international also claimed that the two teams share a similar tactical philosophy, and expects this to make for some tight encounters.
"City has a similar style to Real. It is quick to get the ball forward and looks to directly attack," he continued.
"The strike-force is deadly, as the club has an incredible group of strikers. But if you want to win the Champions League you've got to beat the best teams, and City are one of them."
However, De Gea claims that it is City's individuals, rather than their tactical set-up, that makes them such a daunting opponent, and insists that they have the means to challenge any team in this season's competition.
"It's not about whether the team's style of play will suit Real," he added.
"The team is full of great players, who are very talented and can cause you damage at any moment. They are capable of beating anyone, whether that's Real Madrid or Barcelona."
The shot-stopper highlighted Spain's David Silva as the man who makes City tick, but believes that Real should be very wary of his fellow Atletico old boy, Sergio Aguero.
"David is a vital player for them. City is a different team without him; it doesn't play the same way," he continued.
"But it's not just about Silva. Kun is always up for it and he'll be extra motivated against Real. He's a great player and scores a lot of goals. It's a joy to watch him play."