Hodgson pointed to Chelsea's against-the-odds Champions League triumph last season, when they knocked out Barcelona and then beat Bayern Munich on penalties, as evidence that the fancied sides can be beaten.
He told Sportsweek on Radio Five Live: "You could say we are far from being favourites (for the World Cup) so therefore it's (winning it) not a likelihood. But you've got to shy away from 'impossible' in football."
Hodgson added: "There are plenty of events that we could point to in footballing terms that you could have said were impossible, but people have done it.
"It wasn't likely that Chelsea would become champions of Europe, especially having to change their manager in mid-stream but they did.
"That was by beating Barcelona and Bayern Munich, two of the best teams in Europe along the way, so I'd like to keep that dream alive."
Hodgson took over from Fabio Capello in May following the Italian's resignation and he led England to the quarter-finals of Euro 2012 in his first major championship at the helm.
The former Fulham boss claimed England have enough quality players to challenge the world's top sides.
He added: "I hope that I will never been tripped into saying, 'well, we don't have enough players or there's not enough players good enough to play for England' because that would be a very sad indictment.
"I know there are a lot of foreigners in the league, but there's plenty of English ones. There were seven Englishmen playing for Manchester United the other day and they're top of the Barclays Premier League."
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