Wales international Bale sat out the 0-0 draw against Wigan on Saturday with a nagging hamstring strain which also caused him to miss the defeat by England in a Euro 2012 qualifier.
But such was Bale's improvement in fitness that he was on the point of getting the call at the DW Stadium, only for Redknapp to resist the temptation.
Redknapp said: "I am very hopeful about Gareth. The feeling was if he had have played at Wigan he might have cramped up on his hamstring. So we rested him and hopefully he will be ok for Tuesday.
"I am hoping William will be fit but he is more doubtful. He was not able to train on Friday."
Redknapp has a defensive headache ahead of the trip to the Bernabeu with Alan Hutton likely to miss the rest of the season as he is to undergo knee surgery, while Ledley King, Younes Kaboul and Jonathan Woodgate are also injured.
Source: PA
Source: PA