The Frenchman was the Eagles choice to come into the club this summer, after Oliver Glasner's exit on the back of winning the UEFA Conference League, but he's struggling for positivity in South London.
Just two wins from nine Premier League games, and one victory from three played in the Europa League, has put the club in the relegation zone.
Veteran coach Sean Dyche has been flagged as a possible option to come in, with growing links to Thomas Frank, Vitor Pereira and Robbie Keane, if Sage is moves on.
Palace have two games on the horizon before the international break - at home to Hoffenheim and Liverpool - and the Daily Mirror have added England assistant coach to the list of possible replacements.
Barry has established himself as one of the brightest young coaches in English football, having previously worked at Bayern Munich and Chelsea, as well as in the Belgium and Portuguese national sides under Roberto Martinez.
Thomas Tuchel worked with him at Chelsea and Bayern, and the German appointed him as his No.2 over two years ago, but he's under contract with Three Lions under after UEFA Euro 2028.