Edwards is out of contract at the end of the season, but the club hold an option to extend his deal for a further 12 months.
Wolves boss Dean Saunders is a big fan of Edwards and is keen to keep him at the club.
"Providing we could agree something, I'd like to keep him at the club," Saunders told the Express & Star. "He's a good character, he won't let you down, he's got an eye for a goal and he can play anywhere.
"I've worked with him for Wales and I've seen him score goals exactly like the one he did on Tuesday. He's a good professional, a great lad and he's just got on with it when he's not played.
"He covers the ground, he's a team player and if you ask him to do a job he does it - he doesn't think of himself, he plays for the team. If he doesn't play well, it's not through lack of effort."