The 27-year-old was recently sidelined for around two months with a torn bicep that he picked up during his side's 18-14 win over Leeds Rhinos on May 17.
Green is now planning to be back in action for the semi-finals of the Challenge Cup if the Warriors reach that stage of the tournament.
"I'll be in a sling for two weeks before I get chance to start physio on it," he told the club's official website. "If the guys are lucky enough to get to the semis of the Challenge Cup then that is my aim."
Wigan continue their Super League campaign on Thursday when they travel to Huddersfield Giants.