The 31 year old midfielder joined the Sky Blues in June 2005 and made forty appearances scoring three goals.
The paper says "The Eagles are believed to want the City wideman to bolster their attack as they try to get back into the Premiership at the second attempt. Scowcroft had played for Leicester City under Peter Taylor, who is Palace's new boss."
Scowcroft missed the tour to America through injury but played in the defeat at Halesowen before limping off.