The Sun says Wenger stripped defender Gallas of the captaincy in a sensational showdown yesterday.
And he ordered the Frenchman to stay at home for today's game at Manchester City.
Gallas was "shocked and devastated" and is now considering his future.
A close family member revealed: "Arsene told him 'If you don't want to be in my team then just go. You are free to leave'. William was shocked at the outburst and went straight home.
"He's had the captaincy taken away and has also been suspended from the team.
"Of course, he's totally devastated about what's happened and is now wondering what to do next.
"He simply doesn't know what will happen to him. He's very down."