Hodgson has been a hit at Craven Cottage since taking over a thte club in December 2007.
“Absolutely. There’s no reason not to,” he told The Observer.
“The thing would be to make sure they want me to.
“If I could feel they really want to continue along these lines, and they want me to be the man to do it, I don’t have itchy feet at all.”
He added: “It’s worth bearing in mind. It stops you striving too hard for something you’re not going to get. It keeps your feet more on the ground. Every season, out of 20 managers very few are going to come away with plaudits.
“I’m worried about ceilings, and I’m worried about the constant desire for progression.
“I know you’ve got to progress but you can start reaching too high, and in doing that you can destroy a little bit of the tradition of the club, the structure.”