"I am very happy where I am," said Edwards.
"I have no desire to get involved in the contracts or hiring and firing of people.
"I am a coach and I enjoy being out on the training pitch with the players, so being a director of rugby has never been an ambition of mine.
"At the moment, with me taking over as the so-called 'boss' the only difference has been that I am picking the team and deciding when the subs go on so it has not taken up that much more of my time."
Former Lions No8 Lawrence Dallaglio and former Wasps favorite Dean Ryan, who has been out of work since leaving Gloucester as director of rugby, are among the names being linked with the Adams Park side.