The West Bromwich Albion boss is one of the frontrunners to succeed Fabio Capello with Tottenham manager Harry Redknapp the current favourite for the role often described as one of the toughest in the game.
Hodgson, however, feels that the post could be fruitful. The 64-year-old said: "I don't think any job is impossible.
"England have won a major tournament - only one, but they've still won one - and we are working in a league where football of a very high quality is played and we are producing players who most people would regard as top European standard.
"So, impossible, no."
Asked about being linked to the job, Hodgson added: "I am flattered to be considered."
His Baggies side travel to Premier League champions Manchester United this afternoon.