Tottenham boss Harry Redknapp is the most likely replacement for Fabio Capello, who left the England job in February.
But Hodgson admits he would be interested in the England job, if he was offered the role by the Football Association.
“Of course [I would take the England job], yeah,” he told TalkSport. “I think anyone would. I don’t think there’s a very good reason not to.
“I don’t know if [being England manager] is an ambition as such. It would be an honour of course if ever the offer came my way because, of course, it is the pinnacle of success in a way and certainly a pinnacle of coaching success if ever you’re invited to manage your own country.
“I’ve managed other countries but I’ve never been invited to manage my own [England]. It would be an honour but I don’t have it set out as an ambition as such.
“When you’ve been in football as long as I’ve been and been fortunate to have the sort of career I’ve had, which has also been not just successful but a very enjoyable one, then the most important thing sometimes is to keep that enjoyment, keep that desire to going and enjoy what you’re doing on a daily basis.
“Really, I suppose my ambitions were fulfilled many years ago when I had the success that I had in other countries. I can’t honestly say it’s an ambition but it would be a fantastic honour if ever the chance came my way but it’s not something that I go around thinking about a great deal.”
