Nothing came of the media speculation, however, and Van Aanholt - who joined Palace from Sunderland for £9m in January last year - has declared himself "happy" with life in South London.
"It is always good to be linked with big clubs like Juventus. It is a sign that I am in a good way," he told Sky Sports News. "I am feeling good and I want to keep doing that, but I am a Palace player and I am looking forward to the season.
"I am happy. We have got a great squad, my family lives in London, my kids go to school here. It is just a rumour and unless there is really people coming in then I will never worry about it."
Van Aanholt scored five goals in 28 Premier League appearances for the Eagles last season.