"I told you the other day (I won’t resign) and I’ve nothing more to add," the England manager said before adding: "The FA have asked me to continue. They want me to continue. I’m, very happy that they want me to continue.
"I think there is an interesting group of players here to work with. And I get no feeling whatsoever that any of them will want me to resign.
"I have no reason to do so. I have no intention to do so.
"I don’t want to be compared to other people.
Hodgson will, over the next few weeks, hold discussions with members of Club England – the body that oversees the day-to-day running of the national side.
It is understood that there will be no requirement for Hodgson to submit a full report to the organization regarding England’s World Cup failure, though.
When the "grieving process", as Hodgson put it, is over, the England manager will sit down and analyze videos of the team’s failings in Brazil.
"Our video man will be cutting that up now although he won’t have a chance to show me that for a while," Hodgson said.
Hodgson wants Steven Gerrard and Frank Lampard to continue playing, although he appears open to the idea of resting them for certain matches.
He said: "It would be nice if they don’t formally retire because when players do that they disappear from England selection.
"(We could) leave it to a dialog perhaps whereby at any moment in time I could speak to one of them and say ‘look, do you want to play in this game, are you up for it?’. That’s how I’d really like to see it."