Zidane, who retired after he was sent off in the 2006 World Cup final, was recently appointed "presidential advisor to the first team" by Real president Florentino Perez and the Ajax game will be his first in his new role.
"It's important to all of us to be able to count on Zidane," midfielder Alonso told a news conference ahead of the Group G clash in the Dutch capital.
"It motivates us and he will bring more to the team the more we get to know him better," the Spain international added. "I think his presence at the club is very positive."
Under new Real coach Jose Mourinho the nine-times champions are bidding to end a miserable six-year run in Europe's elite club competition during which they have failed to progress beyond the last 16.
They top the group from Italian side AC Milan and have secured their place in the knockout round.
Milan, who lead Ajax by a point, would join them if they beat French club Auxerre and the Dutch team lost.
"It is very important to us to be group leaders in the next round," Alonso said.
"Usually, being group leaders gives one the chance to play an easier game in the last 16."
