"If it's the time for me to walk away and leave it to someone else, then so be it," Hodgson told British radio station Talksport.
"I certainly won't be looking to walk away from it. But I won't be clinging on when most people are wishing I wasn't there any more.
"It is an important job and football is vital in this country. Lots of people care deeply about the game. You have to be aware that you are looking after this enormous property for an awful lot of fans."
Hodgson's England were knocked out at the quarter finals of Euro 2012 by Italy on penalties and exited at the group stage of the last World Cup in Brazil. They have been drawn with Russia, Slovakia and Wales in Group B of Euro 2016.
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Hodgson said he was happy that whoever manages England through their 2018 World Cup qualifying campaign would be starting in a good position.
"When you take over the job as England manager, you are a custodian," the former Inter Milan, Liverpool and Switzerland head coach said.
"Whatever happens, I will be quite satisfied that I'm leaving a foundation and a group of players and a body of work that someone can carry on."
(Reporting by Simon Jennings in Bengaluru. Editing by Patrick Johnston)
