The 33-year-old defenseman has not played because of a virus sustained in training camp.
"We hope to have him in Friday," coach Jeff Blashill told the Red Wings website after practice Tuesday. "I don't know that yet, but we hope to have him in Friday."
Green, who had 33 points (eight goals, 25 assists) in 66 games last season, joined the Red Wings last week on their road trip and practiced.
"I think we'll assess today and then be in the next couple games," Green said after practice. "It was a good test. I kind of needed to see where I'm at and that was a good way. It was a good skate today."
Defenseman Danny DeKeyser, who has missed Detroit's past four games with a hand injury, could return against the Dallas Stars on Sunday.
The Red Wings (1-6-2) have allowed the most goals in the League (38) and the most goals per game (4.22).
"It would be nice," coach Jeff Blashill said. "Danny and Mike, you can say whatever you want, they're real good defensemen in this league, top four on most teams in the league, and we'd like to have them back."
