The English Premier League club's 1-0 victory over AC Milan at the equally daunting San Siro in February will help the players cope with the atmosphere at Real's giant arena, Redknapp said in an interview with Spanish sports daily Marca published on Sunday.
"We already played very well at an historic stadium like the San Siro against a great team like Milan," said Redknapp, as Tottenham seek to spring a surprise on their first appearance in the modern version of Europe's elite club competition.
"Logically, we know we'll have to be at 100 percent in Madrid for the whole game, which will be very tough, but we are going without fear."
Peter Crouch scored the only goal in the last-16, first leg victory over Milan, which was enough to see Tottenham through to the quarter-finals and came after Gareth Bale netted a stunning hat-trick against the Serie A side's city rivals Inter in a 4-3 defeat in the group stage in October.
"I hope we can give them (Real) a big surprise," Redknapp told Marca. "It's a great day for us and I won't need to motivate the players much, they are all raring to go."
Tottenham are contesting the European champion clubs' competition for only the second time following their debut half a century ago.
Nine-times winners Real are through to the last eight for the first time in seven seasons and could face La Liga rivals Barcelona in the semi-finals if they get past Tottenham and Barca eliminate Shakhtar Donetsk of Ukraine.
Real and Tottenham have both been hit by injuries and a question mark still hangs over whether the Spanish club's Portuguese forward Cristiano Ronaldo will have recovered from a thigh strain in time to feature.
Mourinho said on Saturday after Real's shock 1-0 defeat at home to Sporting Gijon he may risk his compatriot. In-form striker Karim Benzema, who injured himself on duty with France, would not make the squad, he added.
"Do you really think he (Ronaldo) won't play?" Redknapp said in Marca. "I don't. Ronaldo is a fantastic player and I think he'll play."
Tottenham have a defensive crisis and right back Alan Hutton joined the growing injury list on Sunday when he was ruled out for the rest of the season with a knee problem.
Also on the list of absentees are Ledley King, who needs a groin operation, former Real player Jonathan Woodgate (calf) and Younes Kaboul (thigh), while William Gallas (knee) is doubtful.
Vedran Corluka is likely to start at right back with Sebastien Bassong partnering Michael Dawson in central defence.
Midfielder Bale, who has been battling a hamstring injury, should at the least be included in the squad, Redknapp said on the club's website.
"Gareth is OK, not too bad, he's got a chance. He should be fit."
Emmanuel Adebayor, on loan at Real from Manchester City until the end of the se
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1