Before his 22 years at Arsenal, Wenger spent 18 months in Japan as coach of Nagoya Grampus from 1995 to 1996.
The 68 year-old, who left the London club in May, was linked with the national team job before the Japan Football Association (JFA) decided to appoint a domestic coach to succeed Akira Nishino.
According to Sports Nippon newspaper, the JFA could still offer Wenger the post of technical director or even a more unofficial advisory role.
“I met Wenger during the World Cup in Russia,” JFA president Kozo Tashima was quoted as saying.
“He is taking a break from football but we talked about Japanese football.”
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