Madrid have decided to re-sign the 23-year-old Spain international, although his future remains somewhat unclear.
Morata has been linked with big-money moves to the Premier League if Madrid decide to cash in on the forward.
Having impressed in two seasons at Juventus, Morata said there was nothing for him to prove to his hometown club.
"I don't have to prove anything to Zidane," he told Cuatro.
"I'm not a player from Castilla [Real Madrid reserves] to say I've had to earn the opportunity for a pre-season with Real Madrid.
"They will decide if they think I'm ready to be a Real Madrid player.
"I'll give everything to try and fight for a spot and, if not, there'll be another solution."
Morata is at Euro 2016 with Spain and has scored three times, with his side facing Italy in the round of 16.
He said his focus was purely on the national team while they are still in contention in France.
"I don't think a lot about my future because I'm here playing for the Spanish team, trying to win a European Championship," Morata said.
"I think we have to be in this moment. I am calm and will wait and see what happens.
"Right now, I'm a Real Madrid player and I cannot say anything. I would love to join the club but I want to be important in the team and fight for a place."