He said: "I don't think it's something we're contemplating at this juncture. He has just the other day announced he has a hunger to go on forever.
"He won't go on forever, that's an exaggeration on his part, but I don't think it will be my problem.
"I've got another seven or eight years to go (at the club) and it won't be my worry."
But on the subject of Wenger being elevated to boardroom level, a step which some would consider a natural development for a man whose involvement in the club's affairs is comprehensive, Edelman was clear with his reservations.
"He's pretty busy as manager at present. He does attend board meetings, he is a participant to our meetings but he is terribly busy," he said.
"To put that extra responsibility on him when he is running the team - it's unfair to do that. There are lots of responsibilities of directors and extra work and we want him to focus (on the team) at the moment."