Although Tottenham’s Harry Redknapp is the bookmaker’s favourite for the role, the West Brom boss has been linked with the vacancy.
Hodgson told TalkSport: "I don't know that [the England manager's job] 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."
When questioned as to whether he would accept the job should the offer come his way, Hodgson said: "Of course, I think that anyone would."
Baggies midfielder Keith Andrews explained that while the West Brom squad are hoping to keep their manager, the England link comes as no surprise to them.
"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.
"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."
Andrews, a lifelong Liverpool fan, believes Hodgson’s tenure at Anfield should not adversely influence any decision about the England manager’s job, and believes his treatment on Merseyside was "unfair".
"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."
Highlighting Hodgson’s previous international management experience, Andrews believes he would do a "fantastic" job for his country.
"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 finish what he has started at West Brom."