The Frenchman, who in recent weeks flirted with the idea of replacing the sacked Sam Allardyce, says it is “very important” that an Englishman handles the national team.
Wenger also confirmed he had not been contacted by the Football Association, to ask if he was available for the role.
The 66-year-old also made it clear his priority, was to continue at Arsenal where he earns £8million a year.
Wenger, in an interview with beIN Sports, said: “It’s very important [that it’s an Englishman].
“I’ve always said that England has a huge football passion and if tomorrow you have a game with France then it would be difficult [for me] not to sing the national anthem.
“It’s logical. I thought they’d say I’m half English after being here for 20 years! It’s better to have an Englishman.
“It would be difficult to manage another English club team. The national team is different. But my first priority has always been Arsenal.”
Gareth Southgate is temporarily in charge of the Three Lions for their next four matches.