The 22-year-old is due to go back south after Sunday's William Hill Scottish Cup final against Celtic but now says he wants to stay put with Hibs.
Wolves are currently without a manager after sacking Dean Saunders following their relegation to npower League One, but have activated a clause in Griffiths' contract that ties him down to another year in England.
However, the 28-goal striker has made it clear he wants to stay in Leith with the club he supported as a boy.
The Scotland international, who has spent the last 18 months on loan in Edinburgh, has previously spoken about his hopes that Hibs can strike a deal with Wolves but is now more explicit with his wishes.
The Scottish Football Writers' Association and Clydesdale Bank player of the year award winner told Press Association Sport: "It's not 100 per cent definite that I'll be going back to Wolves. I want to stay here. I love the club and I don't want to leave yet.
"It's up to Hibs and Wolves to agree a fee. Wolves have taken up the option of another year on my contract and they want me to be a big part of their plans for promotion next season.
"But I don't want to leave Hibs. It's the fans that I have really taken to because I'm one of them. I've showed on the park how much they mean to me and how much the club means to me.
"I love the club too much to go but if Sunday's match is to be my last, then what a way to go out with a Scottish Cup final and hopefully a winner's medal."