Zidane, 43, has guided Real to the Champions League final and to within a point of La Liga leaders Barcelona since taking over in January.
The World Cup winner with France from 1998 has a contract until 2017.
"We haven't won anything yet and my belief is when you have this job you have to give everything, every day and not think any further," said Zidane.
"We'll see what happens at the end of the season."
Real will meet neighbours Atletico Madrid in the Champions League final in Milan on 28 May. They are third in La Liga, one point behinds leaders Barcelona with two games remaining.
Zidane took over at the Bernabeu after Real sacked Rafael Benitez, now in charge at Newcastle United.
Real Madrid boss Zinedine Zidane says he will wait until the end of the season before discussing his future.