Real have been linked with a move for the Italy international, who is waiting on new contract talks with Juve officials.
"There's a lot written about this subject and there are many rumours. The interest from big clubs does make you happy, but I have no intention of leaving Juventus," said Chiellini.
"I feel very good here and I hope to stay for a long time and extend my relationship with the club. I think we're going to do this in the summer."