Portuguese publication A Bola claimed in June that Ronaldo was keen for a move away after Spanish prosecutors accused him of tax fraud amounting to €14.7million. Ronaldo denied the allegations via a statement from his management company Gestifute.
And Zidane told ESPN on Friday: "Ronaldo is staying and that's it."
The Frenchman reiterated that belief in a media conference ahead of Madrid's friendly with Manchester United at Levi's Stadium on Sunday, but clarified he has never rejected the claims made in the Portuguese press.
"I have not denied the information of A Bola," Zidane said.
"I look at and listen to things like everyone else, but what matters to me is what he wants to do with Real Madrid and I believe he is going to stay."
Ronaldo is not with the Madrid squad for the International Champions Cup, but Zidane confirmed he will return three days before the Champions League holders face United again in the UEFA Super Cup in Skopje.
"He will be back with us on the fifth [of August]," said Zidane.
"He is on a well-deserved holiday after the year we had. He needs to return bit-by-bit and build up his minutes but I am sure he will get up to speed quickly."