Alongside last season's league and cup double, and the 2016 Champions League triumph, Zidane has led Real's first-team squad to silverware success in the UEFA Super Cup twice and the FIFA Club World Cup last summer.
The 21-year-old versatile star rose to fame in the last campaign under the management of Zinedine Zidane and therefore, attracted interest from big teams.
Isco, according to the report, has already signed the new contract which is worth €6m-a-year.
"I know that when we go out onto the pitch we are united".
The title race is set to be even more of a two horse race than in previous seasons as third force Atletico Madrid have been unable to strengthen due to a ban on registering new players until January, while Diego Simeone's side may also take time to bed into their new Wanda Metropolitano stadium.
I'm very happy to have the confidence Real Madrid shows in me. We have worked well and then the goals are always the same - we want to win every game and every possible title.
The French boss and president Florentino Perez are understood to be desperate to keep hold of Asensio as they see him as the long-term replacement for Cristiano Ronaldo but it remains to be seen whether the player can be convinced to stay.
"We're all fit, healthy, physically we're in good condition".
That means Ronaldo should be back in Madrid's starting lineup on Sunday, when it visits Barcelona's Camp Nou in the opening leg of the Spanish Super Cup.
Zidane admitted "there aren't many players" with Neymar's individual qualities, but claimed his absence would not give Madrid the upper hand over the two legs in four days with the second leg of the Super cup to come at the Bernabeu on Wednesday. "If we think it is going to be easier tomorrow we will be mistaken".