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.
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."
He added: "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 (Connor) 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."
Source: PA
Source: PA