Connor took over from Mick McCarthy in February after serving as his assistant but failed to turn around the club's slide down the table and their relegation to the Championship was confirmed last month.
The interim manager will meet with the board after Sunday's final game of the season at Wigan, with his future set to be decided soon afterwards.
Connor, who joined Wolves' backroom staff in 1999, is hugely popular with the players, and midfielder Edwards said: "He's got my vote, that's for sure. He's a great bloke and tactically he's very good.
"But that hasn't been reflected in results and that's down to us as players. If he was given the job and we got off to a good start then I'm sure he'd get us straight back up."
Edwards also echoed the views of fellow midfielder Karl Henry, who claimed players would be more likely to stay at Wolves this summer if Connor is manager.
The likes of winger Matt Jarvis and striker Steven Fletcher are likely to attract offers from Premier League clubs when the transfer window opens.
Edwards said: "There will be offers for players and it's going to be hard for players who want to stay in the Premier League to remain here faced with such an offer.
"I do think if TC was the manager and you knew he was going to be here next season, if you were one of those touted to leave, then he might be able to persuade you to stay.
"He's got that about him and he's got so much respect from the players. That would be in his favour but we'll have to wait and see."
The fans have reacted angrily to Wolves' predicament, though, and Edwards conceded Connor may not be too popular a choice.
"I can totally understand that because if I was a fan and I turned up on a matchday and saw the progression of results, I'd probably feel the same," he said.
"But if the fans want the players' opinions on what goes on behind the scenes, then we think there's no one who loves the club more or who works as hard for the club as TC (Connor) does."
Last weekend's goalless draw with Everton was only the fourth point Connor has picked up in 12 games, and he is still looking for his first victory.
Edwards is desperately hoping that can come on Sunday at Wigan, who secured their Premier League status with a 1-0 victory over Blackburn on Monday night.
The 26-year-old said: "We just need to finish on a high. I keep saying it's for TC, but we haven't given him three points yet and it would be nice if we could finish with two draws and a win to put a better mark on it for him.
"When he has his conversations with the board, it would be nice for him to have a win under his belt."
Edwards was part of the Wolves side that clinched promotion to the Premier League by winning the Championship title in 2009, and he has no doubt the feelgood factor will return to Molineux if they can do something similar next season.
"It was such a great time in the Championship last time," he said. "As great as the Premier League has been, it would be great to replicate what we did in the Championship.
"In my eyes, I haven't had a better season in football as I did in the Championship. It was so much fun. We had that winning feeling from winning every week and we were full of goals and entertaining football.
"It's going to be tough. We know how hard that league is and it's going to be a case of putting in a lot of hard work and determination to get back to the Premier League."
And Edwards, who grew up in nearby Shrewsbury, is certainly not about to turn his back on Wolves.
He added: "Ideally, if I was given the chance to play a part next season, I'd be proud to lead this club back to the Premier League."