The 32-year-old is yet to be confirmed as a bid ambassador but would like to play a role similar to the one which helped London win the 2012 Olympics.
Speaking as he showed Prime Minister Gordon Brown his football academy in London he said: "To bring the World Cup to England would be something special.
"And I would be honoured to be involved in that."
Beckham currently plays for LA Galaxy in America but has 99 England caps and captained his country between 2000 and 2006.
He added: "I was proud to be involved in 2012 and being involved in 2018 is something I would be interested in."
Brown has thrown his weight behind the 2018 bid and said although it was a matter for the FA, Beckham enjoyed respect across the world.
The prime minister said: "David Beckham is known in every part of the world.
"It's a matter for the FA but I'm sure David Beckham will be associated with every big sports campaign that happens in this country because of his reputation, and because of the fame and the respect he has worldwide."
Brown also said that schemes similar to those developed at Beckham's academy in Greenwich could be used to help the Government's target of every child having five hours of sport a week in school.
"I want to see what goes on here having an influence in every part of the country," he said. "It's David Beckham's idea, he thought of this first and it has been a dream come true for him.
"You don't have to be brilliant at sport to benefit from this and you can see what the kids are taking in about nutrition, diet and fitness.
"You can see from the kids that they are listening to what David says. He has support right across the country and what he does as an ambassador for sport generally is something we should be proud of."