Roy Hodgson's side are in desperate need of midfield reinfocements this summer after seeing Yoahn Cabaye and Ruben Loftus-Cheek depart during the close-season.
Loftus-Cheek returned to parent club Chelsea after a successful loan spell, whilst Cabaye joined Arabian Gulf side Al Nasr on a free.
That has left the club woefully short in the middle of the park and according to 'Sky in Italy', Gonalons is the man they want to plug the gap.
The Frenchman is available for transfer this summer after falling down the pecking order at the Stadio Olimpico, making just 16 Serie A appearances last season.
Should Palace land all their targets they could well go into next seaosn with a completely revamped midfielder featuring Gonalons and West Ham's Cheikhou Kouyate, who the club are also believed to be in talks to sign.