The Frenchman has been in change of Arsenal since October 1996 and has a year left on his current deal.
Wenger has now revealed that he has had offers to become an international boss in the past and taking over from Didier Deschamps as France manager would likely interest the 66-year-old.
But despite never taking charge at international level, Wenger has now ruled out any such potential move.
"I think this time [to move into international management] has gone now," Wenger told BeIN Sport.
"I have been asked a few times to do it. I was always busy somewhere else."
France are currently hosting Euro 2016 and face the Republic of Ireland in the last 16 on Sunday.
Wenger hopes Deschamps' side do well in the tournament to bring a 'bit of happiness' back to his country.
He added: "I just want my country to do well and have a good tournament because at the moment this country is going through a very difficult time.
"We have been hit hard through terrorism, strikes and many other unrests.
"The country is a bit flat mentally at the moment, and they need a bit of happiness.
"Hopefully this tournament can give it to the country."
