The 62-year-old is claimed to have turned down the chance to coach Les Bleus on top of his responsibilities in north London, though it may remain a future possibility
Following Laurent Blanc's resignation after a disappointing Euro 2012 campaign, Wenger is said to have been approached by the president of the French Football Federation, Noel Le Graet, with regards to the position.
The newspaper claims that, although the Gunners coach declined the offer, he has left his options open regarding potentially assuming a dual role at some point in the future.
The FFF's first choice, Didier Deschamps, has also reportedly rejected the chance to take over and now Montpellier manager Rene Girard has also dismissed reports linking him to the vacant post.
Between 2002 and 2008 Girard took charge of the national team at various youth levels, including four years with Les Bleus' Under-21 side, but he is unwilling to resume working with the national administration.
"I know the house [the national set-up]. They made me go, there is no reason that I would want to return," he told RMC Sport.
Girard guided Montpellier to its first-ever Ligue 1 title last season and the club will compete in the next edition of the Champions League.
Current Oman coach Paul Le Guen and Francis Smerecki have been suggested by L'Equipe as other possibilities to take on the role but it is also speculated that Le Graet could take longer to make an appointment.