The former Liverpool man has been a mainstay for Wolves since Nuno took over the dugout.
Edwards said: "Conor has always been a leader. He's so vocal – such a big talker.
"He's like that every single day in the dressing room, and such a happy guy as well, always having a smile on his face.
"That raises the energy in training and around the place, even when you've lost a game.
"Conor was the natural choice for Nuno, and he has revelled in the centre of defence.
"It was a natural option. He can see the pitch from there and organise.
"He has been a leader since he was a teenager, captaining England at youth level. I just hope he gets a chance at senior level with England now."