Wright is one of the former Gunners players, to hit out at the German playmaker, after a string of avertage performances this season.
Ozil fired back during the international week and manager Arsene Wenger also criticised some of his former players, insisting they also had struggles during their careers.
“My legendary status got revoked by some people on Twitter. I told them about themselves,” Wright said on Match of the Day.
“I’m not a legend anymore, apparently.”
Asked if he would like to make amends with Arsenal fans, he responded: “I’m not shaking anyone’s hand.”