Petterson has been out since March 2 with an injured wrist. The Canucks have five games remaining this season, the most in the NHL.
"He's been pushing hard to get back. I'm not going to get into the specifics of the injury right now," said Green, according to Sportsnet 650's Brendan Batchelor.
Prior to suffering the injury, the 22-year-old posted 10 goals and 11 assists in 26 games this season. In 2019-20, he finished second in team scoring, behind forward J.T. Miller, with 66 points (27 goals, 39 assists) in 68 games.
The Sundsvall, Sweden, native is scheduled to hit restricted free agency this off-season alongside Canucks star defenceman Quinn Hughes.
Vancouver plays the Calgary Flames tonight at 9 p.m. ET/6 p.m. PT on Sportsnet.