Netherlands international Van Aanholt hit five goals from left-back last term as Palace recovered from a dreadful start to stay in the Premier League.
And the former Sunderland defender shrugged off suggestions he could look to leave Selhurst Park for Turin before Thursday's transfer deadline.
"It is always good to be linked with big clubs like Juventus. It is a sign that I am in a good way," Van Aanholt said to Sky Sports.
"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."