Chances were few and far between in the first half but Madrid could twice have taken the lead as Marco Asensio scuffed his finish after being put through by Isco and Raphael Varane's shot was blocked after a goalline scramble.
"All of my players are important and good, but we are going to make changes", Zidane said on Sunday.
While for Leganes the draw extends their unbeaten streak to four league games, but have not defeated Madrid in league play in the last six matchups.
The defensive midfielder did not have many chances when Zinedine Zidane was manager last season despite the Frenchman heavily praising his performances from the loan stint at Deportivo Alaves in 2016/17. "Even if this might have been a bad season, we must all give a bit more".
However, Unai Emery's men held out for a first clean sheet away from home in the Premier League this season to move ahead of Chelsea on goal difference into fourth. "He is a fantastic player and this year what has changed is that he has scored many more goals, so I am happy for him".
Gareth Bale was introduced as an 81st-minute substitute and made little impact.
"We're always willing to win and we've got our pride, our love for the shirt is worth a lot more, and we have to demand more wins and better results from ourselves".