The Frenchman has delivered European titles in his first two seasons to make the Spanish side the first ever to win the competition consecutively in its current format.
Madrid are just one game from reaching another Champions League final as they hold a 2-1 lead over Bayern Munich heading into the second leg of their semi-final on Tuesday, but their domestic struggles have led to speculation surrounding Zidane's future.
However, Zidane insists he will not be sacked if he fails to extend their reign as kings of Europe.
"My future is not depending on what happens in the Champions League," he told reporters.
"You all know I am the coach now and I want to continue, but this is not the most important thing at the moment."
Zidane took time to congratulate Ernesto Valverde's men before the upcoming Clasico on Sunday, but was anxious to turn attention to the midweek game at the Santiago Bernabeu.
"We are going to try to win the game against Bayern. That's the objective," he said. "We are not going to speculate, defend, or any similar strange things... we have to try to score quickly.
"In La Liga, Barcelona are the clear dominant force. They were deserved champions. We have to congratulate them.
"They have won two trophies and it's a great season for them, but now we are just thinking about reaching the final."
Madrid will be without Dani Carvajal for Tuesday's match against Bayern, while Isco is a doubt after picking up an injury and Nacho could return, but Zidane is not rushing to decisions over whether the latter two will feature.
"It's important they are 100 per cent fit. We will decide on Tuesday," he said. "Nacho has been out for a month, but he has been training a lot, even though he trained just twice with us.
"If they are in the squad, it is because they are 100% fit. They have different injuries. Isco knows what to do. We all want to be in that game.
"And we are going to do everything in our hands for him, but without risking his health."