The World Cup winner replaced Rafael Benitez in the Santiago Bernabeu hot seat in January and led them to glory in the Champions League -- the 11th time they have been crowned Europe's best club team.
Zidane was unable to deliver the La Liga title, though, as Real Madrid finished a point behind Barcelona, and the new campaign has brought fresh challenges.
After an impressive start that almost saw Madrid equal Barcelona's record 16-game winning run in the top-flight game with a 2-0 victory over Espanyol, they have not won since.
Madrid have drawn four successive games -- three in the league and one in the Champions League -- and the pressure on Zidane has begun to build.
"I'm not afraid of being fired," he was quoted as saying by the club's website on Thursday. "Anyway, it will happen."
Zidane said, "I thoroughly enjoy what I do. I have an incredible opportunity, I am happy with what I do. I enjoy my job, which is not always easy."
"But I want to learn and advance. Working with these great players I learn every day. I am dedicated to what I do on the field. What is interesting to me is the week (of training), more than the matches."
Zidane added, "I have an exceptional group, whether we win or we lose, they are good people."
Zidane believes Madrid's current problems are more psychological than physical, and he is confident he will be able to find a solution to get them back to winning ways.
"What's important is to find solutions and I'll find the solution. There is nothing catastrophic, but it's not trivial," he said.
"I don't think it's a physical problem. It's the first minutes of the games that are penalising us. The content of these games in La Liga were very bad, especially against Villarreal."
"It's psychological. We are trying to find the problem."