The 65-year-old coach has admitted that the Three Lions will head to Brazil as outsiders but claims that the Blues have shown that unfancied sides can topple tournament favourites
The former Liverpool boss admitted that the Three Lions are "far from being favourites" to win World Cup 2014 in Brazil but refused to rule out their chances.
Spain have dominated the international stage in recent years but Hodgson pointed to Chelsea's shock results against Barcelona and Bayern Munich in Europe's premier competition as cause for optimism.
"You could say we are far from being favourites [for the World Cup] so therefore it's [winning it] not a likelihood," he told the BBC. "But you've got to shy away from 'impossible' in football.
"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 pointed to the strength of the Premier League as proof of the potential of the England national team despite the amount of foreigners starring in the country's top flight.
"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," he continued.
"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.
"I hope I'm not going to be tricked into saying that some time to disguise my disappointment in a defeat or to try and shift the blame to somebody else."
The 65-year-old did admit, however, that the pre-tournament pressure placed on the players by the English media and public could have an adverse effect on the Three Lions' younger players.
"I would like to see a little bit more kindness sometimes offered to the players, because there's no doubt in my mind they are as aware as anybody we need to win, we need to bring something back to the English public," Hodgson explained.
"But sometimes if you put so much pressure on these young people there's no doubt they can be hampered by that rather than encouraged.
"And it's that delicate balance of having the expectation which propels you forward because you want to succeed and you want to show people you can meet their expectations or freezing a little bit because you feel, 'whatever I do is never going to be good enough'."