The Dutch side go into their final Group D game third in the standings, with no chance of catching the top two and focused on protecting their one-point lead over Manchester City, who travel to Borussia Dortmund.
Last season, Ajax saw their hopes of reaching the last 16 ended by Real with a home defeat and they have struggled to find success in Spain over the years.
And Frank de Boer has received a blow ahead of the Real game after it was revealed Ryan Babel had suffered a setback in his recovery from a dislocated shoulder.
Babel picked up the problem against PEC Zwolle on November 11th and was expected to be out for six weeks, but he may now be missing until after the turn of the year.
"I will be back after the winter break," Babel told De Telegraaf. "The injury itself is not so bad but with shoulder injuries you have to be careful."
Danny Hoesen, who scored in Ajax's 3-1 victory over PSV at the weekend, could be handed a start in place of Babel.
Real are guaranteed second as they cannot win the group due to their head-to-head results with leaders Borussia Dortmund, so Jose Mourinho could decide to change things around for the Bernabeu clash.
Defender Alvaro Arbeloa is suspended and could be replaced by Raphael Varane while midfielder Xabi Alonso may be rested after playing a lot of minutes in recent weeks.
Luka Modric could fill in for Alonso by dropping further back into midfield while defender Sergio Ramos might also be given a break.
It is unlikely that Mourinho will want to finish off the group stages with anything but a flourish, so Cristiano Ronaldo and Karim Benzema could still feature.