In a damning attack Petit, who played with Cole at Chelsea in the 2003-04 season, has accused Cole of being mentally weak.
Petit, 40, told The Sun: "I'm not convinced. I played with him a few years ago. He is a player who can sometimes have moments of class but he is too inconsistent.
"He is often injured - mentally very fragile. He's warmed the bench wherever he's been."