Football star ran down his contract, according to local media, and was unable to agree an extension after Real offered him a one-year deal on a 10% pay cut which he rejected.
Zidane’s departure comes at the end of a disappointing campaign for the 13-time European champions.
Spanish media are reporting that Real Madrid coach Zinedine Zidane informed the players about his exit at the end of the season.
The Blues ousted Los Blancos 3-1 on aggregate after a 2-0 victory in the second leg of their semifinal.
Jose Mourinho has been sacked by Tottenham just six days before they play Manchester City in the League Cup final, the club announced on Monday.
European football's governing body UEFA says players from the 12 major clubs could face international exile while calling splinter league "a cynical project... founded on the self-interest of a few clubs".
The 74-year-old has been officially re-elected as president of Real Madrid until 2025 for a fifth consecutive term and sixth overall.
Karim Benzema put the champions in charge at a soggy Alfredo di Stefano stadium with a delightful backheel in the 14th minute while a deflected Toni Kroos free-kick doubled their lead in the 28th.
"If you want to go to the semi-final, you have to earn the right to do so. We didn't do that tonight, especially in the first half," Liverpool coach Juergen Klopp said after the team's Champions League quarter-final match.
Coach Zoran Mamic quits days before a Europa League clash with Tottenham as Croatian Supreme Court confirms prison sentence.
Real Madrid are back within touching distance of the top of La Liga after they punished another Atletico Madrid slip against Levante by beating Real Valladolid 1-0.
Real Madrid coach Zinedine Zidane expressed his annoyance with his side's growing injury problems after a setback to defender Dani Carvajal in their 2-0 win over Valencia left him with eight stricken players at a crucial stage of the season.
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