The Three Lions have not reached the final four of a World Cup since 1990 and have won the tournament just once, in 1966, but, despite their sitting 10th in the world rankings, the former national captain expects them to be aiming high.
"I'm always optimistic about when England go into competitions because I've been there, I've felt how it is when you go into a big competition," Beckham told Sky Sports News.
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"I think you always go into competitions thinking you're going to win it."
The former Manchester United and Real Madrid midfielder acknowledged the size of the task facing England but picked out Tottenham winger Andros Townsend as an example of why Hodgson's men can shock the footballing world.
"It's obviously very difficult because you come up against some of the best countries with some of the best players in the world," Beckham added, "but we have some young players coming through like Townsend, who has come into the team, and there's a freshness now. He is playing without any worries and that's great to see.
"He's a player who hasn't always been in the starting line-up, he's gone out on loan a few times but he's now one who's established in the England team.
"This is the biggest football competition in the world, with the best players in the world, but we'll see. I hope we can go all the way."