The Frenchman suggested he may accept the job but warned the Football Association that he would only do so once his current contract with the Gunners runs out in 2017.
"Could I manage England? “Why not?" the 66-year-old told reporters. "I would never rule that out, but I am happy and focused in club football.
"I have one more year to go with Arsenal and I have been with them for a long time. I have always respected all my contracts and will continue to do that. What will I do after that? Honestly, I don't know.
"England is my second country. I was absolutely on my knees when England went out against Iceland. I couldn't believe it."