The Football association is currently searching for Roy Hodgson's replacement following his resignation in the wake of England's disasterous Euro 2016 campaign.
Sunderland manager Sam Allardyce and Hull City's Steve Bruce have already been interviewd for the job with Eddie Howe and Jurgen Klinsman the other top candidates.
However, Cole believes that Wenger, who has one year left on his Gunners contract, would be the ideal man to lead England.
"I don't know going forward, should they go with a foreign manager or stick with an English manager? It's debatable. Personally I would like to see Wenger in charge," said the LA Galaxy defender.
"He is good with the youngsters, knows how to win and knows his football. If I had to choose a manager, it would be Wenger.
"He could take the team to the next level. There is a lot of talent and they need a bit of experience.