The London club are aware that manager Roy Hodgson is not a long term option.
With the veteran likely to retire at the end of the season, Palace may then turn to Cooper.
Per talkSPORT, the club's chairman Steve Parish is a huge admirer of the work Cooper has put in at Forest.
Against all the odds, he has gotten them promoted to the Premier League and survived at the first time of asking last term.
Cooper is still under pressure at Forest, given the expectations of owner Evangelos Marinakis.