The Turkey international is expected to sign a new deal from 2029 to 2030.
But ahead of Thursday's Club World Cup clash with Manchester City, Yildiz said: "I'm honest, I'm not thinking about it at the moment. I'm happy with the situation and I'm only interested in working for the good of the team.
"I don't talk about money, I want to give my all on the pitch. Does John Elkann have a soft spot for me? We've talked a bit, I know he appreciates the way I play. He's a beautiful person, he even wrote me a wonderful message in the last few days, it was very nice."
On the Club World Cup, he also said: "They are crazy sensations. You feel important when you experience these emotions, but my only thought is to stay focused on our objectives. The rest will come by itself. A player who intrigues me the most? There are many, for example in Real Madrid.
"Arda Guler is very strong and will have a great future, it is nice to be compared to them. But don't ask me who I consider the strongest, I won't say anyway..."
Yildiz was also asked about the toughest defender he's faced and added: "There are many good ones, starting with those at Juve, but if I have to name one I'd choose Van Dijk: he's very strong."