Hodgson remained in the hot seat despite a disappointing World Cup in Brazil last year where his team failed to win a match and exited at the group stages.
Since then England have made a solid recovery by winning six consecutive matches, including all four qualifiers for next year's European Championship.
Recent reports suggest that Hodgson was keen to stay on with the national team until 2018 and have another crack at the World Cup, but the former Inter and Liverpool boss is in no rush to put pen to paper.
"What I really want to do is to make certain is that I do the job I'm currently contracted to do to the best of my ability and hope there are no slip-ups," he said.
"I hope when we go to France - and I believe we will qualify - we will give a good account of ourselves. I don't need to look beyond that at the moment.
"I am happy with my life and where we are as a team. The memory of the Wold Cup will always live with us but I hope to some extent we are putting it behind us.
"We'll see about [going to another World Cup]. It is a magnificent job being England manager and I'm really pleased to have the chance to do it.
"My employees seem comfortable with me and that's enough for me. At this stage of my career I don't look any further. I don't want to outstay my welcome, that's for sure, so we'll see what happens."
England return to action against Lithuania on March 27, with Hodgson's side looking to make it five wins from five in Group E of Euro 2016 qualifying.
