The 42-year-old, who had a four-year spell at Los Blancos arch-rivals Barcelona during his playing career, thinks that despite the odds being stacked against his side, anything is possible if the players believe in themselves.
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"It is all about believing in yourself. Against Real Madrid last year, and Manchester United, we've shown that we are able to keep up,"
"We must be very careful with the ball when we have possession. We did well last weekend against FC Twente, as they were waiting for us to lose the ball.
"But Real Madrid are so effective on the counter. That was very clear last year at the Bernabeu when they beat us 3-0."
When asked whether he thought the Madrid coach Jose Mourinho would be side-tracked by the prospect of El Clasico on Sunday, de Boer said: "The Champions League is really important for them. Last year they won the title in La Liga, and now they're aiming for this title.
"I don't think Real and Mourinho are thinking about El Clasico. The press does, but that does not mean that they do too."
Ajax's Champions League Group D match against Real Madrid kicks off at 20:45 at the Amsterdam ArenA.