The Turkey International has been associated with a move to England, where Arsenal and Liverpool champion are the clubs.
But La Gazzetta Dello Sport says that Elkann has a “weak” for Yildiz and does not want to see him leave this summer.
Yildiz was sent in the victory over Monza and Juve coach Igor Tudor last week about the playmaker of midfield: “He is a good guy and he really gives a lot about it. He is in love with football.
“He is pure and I understood what he did. I saw the video, he was pulled, he wanted to come loose and made that gesture. It was not malignant, but he paid for it.
“I want to emphasize his kindness, which is important. He has never done anything like that. It will be a lesson for him.”