Di Stefano was the face of Real´s domination during the 1950s and 1960s, when they won five European Cups and he scored more than 300 goals.
Ronaldo is now trying to lead another prolonged period of European success, with Real gunning for their third consecutive Champions League triumph, and fourth in five years.
They take a 3-0 lead into Wednesday´s quarter-final second leg at home to Juventus after the Portuguese scored twice last week in Turin, a double that included a sensational bicycle kick.
Ronaldo already has 14 goals in this year´s tournament, three short of his best ever 17, which he posted when Real were crowned champions in 2014.
“I do not think of playing without Cristian, we have him and we are happy,” Zidane said on Tuesday.
“There are many people who remember Di Stefano, it is normal – many people, and I am one of them, will now remember Cristiano with this club.
“We have him and it is necessary to take advantage of this. All the teams in the world would be happy to have this player.”
Barring a huge collapse at the Santiago Bernabeu, Real will take their place in next month´s semi-finals but their domestic season has been far less impressive.
Real sit fourth in La Liga, 15 points behind Barcelona, while a shock defeat to Leganes in the Copa del Rey means they have only one chance of a major trophy.
“The explanation I do not have,” Zidane said. “Sometimes this year our consistency has not been very good.
“We have had moments of difficulty, now we are better, but there is no explanation. If you ask me, I have more motivation than I can ever remember to win the league. It is the hardest thing to do, it is what the player wants.
“There are difficult times but in the Champions League, when you look at the trajectory of this club, it is impressive and nobody has reached this level. It is what this club has.”
Real have hit a golden patch in recent weeks, losing only one of their last 15 matches and scoring 20 goals in their last seven.
“When we scored again, with three or four goals, you cheer up, you feel better, you have your confidence back,” Zidane said.
“But it annoys me when people say we are favourites in the Champions League. We are a great team but we have won nothing yet.”
Real will be without the suspended Sergio Ramos for the return game against Juve, meaning 21-year-old defender Jesus Vallejo could come in alongside the more experienced Raphael Varane.
Varane insists he will not look to make up for the loss of Ramos´ leadership at the back.
“My preparation for the match does not change,” Varane said. “I have my personality, I know how to guide my partners, to speak to the team.
“But I will not transform into someone who will bark orders. I will do it with personality, as usual, and the important thing is that the team can rely on me.”