England, who are already 28/1 outsiders to win the tournament, will learn their opponents in the group stages of next summer's tournament in today's draw.
FIFA rules dictate that Hodgson cannot put a wager on next summer's tournament.
However, when he was asked by reporters if he would put £10 on hosts Brazil, Hodgson answered: "No. I'd put it on England.
"I'd have a chance of losing it on Brazil so why not put it on the team I want to win it?
"We all know the result everybody wants and that's to repeat 1966. We all know that's not going to be easy but it's great to be there trying to do it."
England have struggled in their away qualifiers and they were booed off twice last month following defeats to Chile and Germany at Wembley.
But, as he spoke to the media by the pool at his hotel in Salvador on Thursday, he was full of optimism.
England, he said, currently have a well-balanced squad with the right mixture of youth and experience, with several pacy wingers capable of cutting open defences on the counter.
"Over the last 19 months the thing that's pleased me most is the emergence of us as a counter-attacking threat," Hodgson added.
"I think we've got a much bigger counter-attacking threat than we had a couple of years ago because of the pace of the players.
"Gareth Southgate is spoiled for choice with wingers in the Under-21s.
"Then, of course, you have the Townsends, the Welbecks, the Sturridges, the Walcotts, the names go on and on, really."
Sky Sports will bring you all of the news from the World Cup draw in Brazil live on Friday from 4pm - online, on mobile and on Sky Sports News.