England will also face Slovakia, Slovenia, Lithuania and Malta in Group F, but the England manager’s current contract expires after the Euro 2016 finals next July, before the World Cup qualification process begins.
However, the 67-year-old says he wants to be given the chance to lead England to Russia.
“It’s not something I want to give up lightly, but if the FA want me to stay on I would be delighted to do so,” Hodgson told Sky Sports News HQ.
Speaking after Saturday’s qualification draw, Hodgson also called for England’s upcoming games against Scotland to be played in the “right spirit”.
“It is a very fierce rivalry and that’s good, (but) it’s not fierce on the field as the games are played in absolutely the right spirit,” he added.
“For the mass media, it’s the fixture that is going to capture the imagination. England v Scotland fixtures go back a long, long way in history and there has been many a fierce encounter along the way.
“Let’s make certain we keep talk of fierce and intense rivalry to the many fixtures back in the past that people refer to.”
The two sides have not played each other in a competitive game since qualification for Euro 2000 in 1999, but England have beaten Scotland twice in recent friendlies.
“Both the games at Wembley and Celtic Park were played in a very competitive manner and were extremely intense, but there was certainly nothing untoward,” Hodgson added. “There was not a bad foul in either of the two games.”
However, Hodgson insisted that Scotland are not the only team that England will be thinking about, rejecting suggestions his side should be regarded as automatic favourites to win the group.
“Slovenia are a good team, as are Slovakia. Lithuania and Malta are experienced at this level so I think it will be a very competitive group,” he said.
“We need to be careful before we start describing ourselves as overwhelming favourites. We have to make certain we respect all our opponents and remain fully conscious that every time we don’t go on the field and do our job to 100 per cent, we could lose.
“We are happy with the group. It’s just a question now of trying to make certain that the players can handle it.”