Boss admits his side must perform better but faces defensive challenge as French centre-back is set to join King, Kaboul and Woodgate on the injury list
Bale was rested for the goalless draw against Wigan on Saturday and was ruled out of England’s vital 2-0 victory against Wales in the Euro 2012 qualifier due to the recurring strain.
Redknappp almost put down the winger’s name on the team sheet but decided to change his mind for the game against the Latics.
The 21-year-old should return to action at the Bernabeu for the quarter-final first leg.
However, Redknapp is without his regular back four as Younes Kaboul, Ledley King and Jonathan Woodgate are all ruled out due to injury as well as Alan Hutton who has to undergo surgery on his knee and is set to miss out on the rest of the season.
French defender William Gallas could also miss out on the encounter with the Spanish champions because of a knee problem.
The Spurs boss told reporters: "I am very hopeful about Gareth. The feeling was that if he had played at Wigan he might have cramped up on his hamstring.
"So we rested him and hopefully he will be okay for Tuesday.
"I am hoping William will be fit but he is more doubtful. He was not able to train on Friday.
"We have a big week and a massive game to come on Tuesday, so we will see how we go.
"Of course it will be a tough game against Real Madrid. We will have to play better than we did at Wigan if we are going to get the result we need there."