The 22-year-old, who moved to Wolves from Dundee on a two-and-a-half-year deal in January 2011, has scored 14 goals in the Clydesdale Bank Premier League this term, including the winner against Celtic on Saturday. His current half-season loan deal is due to end in January.
The boyhood Hibs fan, who also spent last season on loan at Easter Road, told the Edinburgh Evening News: "I have told them I want to stay so now I just want it done as quickly as possible but I need to wait and see.
"We still have a big game coming up on Thursday (against Hearts) then we have a two-week break. If it doesn't happen by then my last game will be at home against Dundee (on January 19).
"They are speaking, so I am hoping it's done in the next week or so."
Hibs boss Pat Fenlon's winter transfer window priority is extending the loans of Griffiths, Manchester City defender Ryan McGivern and midfielder Jorge Claros, whose parent club is Honduras' Motagua, but the Irishman knows the final decision lies with the parent clubs.
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- Clydesdale Bank Premier League