"England is my second country", he said. "I don't know, but England couldn't find an answer to what Iceland posed".
Wenger has been one of a number of names to have been linked with the job, but the Frenchman insists he will not break his contract with the Gunners, which runs until next summer.
FA chief Martin Glenn has suggested he would be willing to wait for the right man and appoint an interim manager, though England U21 boss Gareth Southgate has ruled himself out of the running having previously been considered a strong contender. I couldn't believe it.
But Wenger, speaking to Bein Sports in France admitted he is no longer averse to managing England.
'But when you watched the game you could sense, after 60 minutes, that the worst could happen.
"Fair play to Leicester, Leicester won it hands down, but it was the best chance Arsenal had had in many years to bring the Premier League title to the Emirates and it went missing". Did they panic or were they exhausted? I have always respected all my contracts [throughout my career] and will continue to do that.
The 51-year-old former Tottenham striker has been sounded out as the race to replace hapless Hodgson heats up. "Honestly, I don't know", he said.
"The success of the story is the high quality but also the good organisation and good atmosphere we have in the group". The FA are expected to make an appointment in the coming weeks so that Hodgson's successor will have been installed in time for the World Cup 2018 qualification campaign that begins in September.