A three-man panel of the Football Association staff began the job of finding Hodgson's successor last month.
"Could I manage England? Why not? I would never rule that out, but I am happy and focussed in club football," Wenger told British media.
"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.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"England is my second country. I was absolutely on my knees when England went out against Iceland."
Wenger, who led Arsenal to second in the league table last season, took over as manager in 1996 and has led them to a top-four finish in every season since.
England's under-21 manager Gareth Southgate, the bookmakers' favourite to be the new England manager, was tipped to take over on a temporary basis but is apparently not interested in the job.
According to local media, Sunderland manager Sam Allardyce will be interviewed for the job this week while U.S. head coach Jurgen Klinsmann's name is also doing the rounds.
(Reporting by Ian Rodricks in Bengaluru; Editing by Amlan Chakraborty)
