It has been reported by the British tabloid that City manager Pep Guardiola wants Van Aanholt as cover for Benjamin Mendy, who is on the sidelines at the moment with a cruciate knee injury.
The report has also claimed that Palace could sell the 27-year-old left-back in order to recoup the £12 million fee they paid Sunderland.
As reported by The Sun, Palace signed the Netherlands international from Sunderland in January 2017 for £12m.
The Black Cats signed the left-back from Chelsea in 2014 for a transfer fee reported by The Sun to be worth £1.5m.
Van Aanholt played well during his time at Sunderland and has proved himself in the Premier League.
The Black Cats are in danger of getting relegated to League One at the end of the season, but the Dutchman could well be lifting Premier League as well as Champions League trophies this term.