The 68-year-old recently told reporters that he is not too old for another big job and worries about clubs discriminating against him because of his age.
One club who are understood not to feel this way are Everton, who have reportedly made regular inquiries about Wenger's availability, according to the Daily Star.
It has been suggested that the club are looking to replace unpopular boss Sam Allardyce this summer, even though Allardyce recently told reporters that Everton have the potential to be a Champions League club in years to come.
Former Arsenal vice-chairman David Dein is understood to be the middle man in any talks between Everton and Wenger, as he is good friends with the 68-year-old Frenchman.
However, Wenger is undecided as to whether he will carry on as a manager or move into a career as a sporting director. He is worried that his age could restrict him, but says he still feels good and wants to continue.
“I don’t look very good on the beach," Wenger told reporters at a recent press conference. “I don’t know how long I can carry on. How long would I like to? As long as I feel I want to.
“But overall people look at your age and make an issue of it. It becomes a bit discrimination. They don’t really look how you work and perform. They look and say, ‘Oh, he is old’. I can understand that as I thought the same when I was young.
“But who knows? I like the English saying, ‘You have to live every day like it is your last – and one day you will be right’.
“I keep myself fit. I can still play! I don’t play with the -players, they are a bit too quick for me. We have staff games.”
When asked how many offers he has had since announcing his resignation, Wenger simply replied: "More than expected."