He added: "I don't know that it is an ambition as such. It would be an honour of course if ever the offer came my way, because it's the pinnacle of success in a way and certainly of coaching success if you are ever invited to manage your own country."
Hodgson's candidacy would be stronger were it not for an ill-fated spell with Liverpool that saw him last only half of the 2010-11 season.
However, West Brom midfielder Keith Andrews - a Liverpool fan - feels he would be the perfect successor to Fabio Capello.
"We all hope Roy Hodgson stays at West Brom but he is linked with England for a reason, the reason being he is very good at his job," Andrews said. "If you ask the players here, or players who have played under him at previous clubs, all the feedback is so positive and his enthusiasm and love for the game is very infectious.
"People should not be put off by what happened at Liverpool. I'm a Liverpool fan and I was delighted when he got the job.
"Only the FA will know how much that spell has altered their view on him. I thought he was unfairly treated, and the circumstances and the timing wasn't great when he went into the club.
"It was certainly a transitional period at Liverpool and didn't quite work out but you look at his pedigree and the experience he has, he is an ideal candidate for England.
"He has managed at international level before, he has got the pedigree and personality for it, he can deal with players, and deal with the personalities. If chosen, I'm sure he could do a fantastic job but hopefully he can stick with us and crack on and finished what he has started at West Brom."