Victories in both matches on October 11 and 15 at Wembley would ensure automatic qualification for the 2014 tournament in Brazil, however the Three Lions drew three of their five matches over the summer - most recently a 0-0 stalemate against Ukraine in Kiev last month.
But former England captain Beckham has no doubt that Hodgson's group have what it takes to reach next summer's showpiece.
"I do," the Sky Sports Ambassador replied when asked if he thought the England squad were winners.
"There's a transitional period that was always going to happen. You see it throughout sport, you see it throughout teams and countries and obviously Roy Hodgson has come in and done a good job.
"There's a lot of young players in the team and we've still got those players that they can look up to like Frank Lampard, like Stevie G (Steven Gerrard). There's players in there that have been in there for many, many years who have experienced World Cups and big games.
"So they have got those players that have got the experience in there, but young players will only learn when they're playing and that's what Roy has done. He's brought in a couple of young players that are the future of English football."
Beckham, who retired from competitive football following a short stint with Paris St Germain last season, added: "I think people like to see winners and see teams and the country you support and live in be the best.
"That's why we are a country of believers and there are high expectations in our country.
"Whenever we go into a competition, whether it be football, whether it be any other sport, there's always high expectations and that's rightly so, because we're a country that's passionate about our sport and we're believers and that should never change."
The 38-year-old reckons the past 18 months have stoked the fire of the country's collective sporting passion, with unprecedented success at the London Olympics and Paralympics, in the Tour de France and at Wimbledon.
Speaking at a Sainsbury's Active Kids event in east London, he said: "The actual lead-up to the Games, there was so much anticipation, so much excitement and then once the Games began, the fact that we were so successful through those Games, it just added to the excitement and the pride that we all had to actually see our athletes perform as they did.
"That's when we go back to the children. Children watching the Games, children going to the Games, being able to see these athletes perform and win gold medals and win the medals that we won - it doesn't get better than that.
"It was a proud year for us as British people. It doesn't get any better than the year that we had."