The teams meet in Dubai before returning to action in their respective league campaigns in the new year.
Milan currently sit seventh in Serie A, but Montolivo is hopeful a positive result against Real could aid a push for the UEFA Champions League positiions.
"This game can give the team a big lift," he said. "I think it's a great 'training' match if I may say so because, when you face teams like Milan and Real Madrid, there are no friendly matches.
"A game like this helps us to immediately hit the ground running when we return to league action.
"It will also be a good test to see where we are when we come back from the winter break.
"We've been lacking a bit of consistency, but it’s normal for a team that is rebuilding.
"I believe that we've seen steps forward recently in terms of solidity and the group, and the match with Real Madrid is an excellent chance to test ourselves once again."
Milan face Sassuolo in Serie A on January 6.
