The Spain striker, 23, returned to the Bernabeu earlier this summer on a £25million buy-back option from Juventus.
Reports suggested the LaLiga giants only activated the clause in order to make a profit with an instant sell-on, starting a bidding war with a number of parties interested across Europe.
Among those teams linked is Arsene Wenger’s Gunners – who also appear to be chasing Gonzalo Higuain – and Antonio Conte’s Chelsea, as the debate continues about his exact role within the Madrid squad.
Zidane, though, gave no suggestion he was ready to quickly offload the player.
Speaking at a press conference in Canada ahead of the International Champions Cup, Zidane said: “He is another member of this team.
“He’s back and I’m happy to have him.
“He is an academy product, who knows what Real Madrid is and truthfully we are, and me above all, happy to have him with us. Later we’ll see…
“We have a large squad and all the players will be important. Alvaro will be one more of the team.”
Zidane also played down questions over the roles of Colombian midfielder James Rodriguez and youth product Jese.
“A large squad gives you a few more problems but that comes with the territory as Real Madrid coach,” he said.
“I have to play the most competitive side I can and I’ll do the same thing this season, that’s my responsibility.”