The programme accused three members of the Fifa executive committee - Nicolas Leoz, the president of South America's Conmebol federation, Confederation of African Football president Issa Hayatou and Brazilian Football Confederation president Ricardo Teixeira - of taking payments from a company that was subsequently awarded lucrative rights to the tournament.
Fifa vice-president Jack Warner, who will also vote on Thursday, was accused of attempting to sell World Cup 2010 tickets with a face value of £54,130 ($84,000) on to the black market.
Warner has brushed off the allegations, telling reporters: "I really have no interest in this matter... now or ever."
Beckham stated that Blatter had not been annoyed by the programme, but had raised it in discussions with him.
"He just mentioned it in the talk we had. Obviously it is not the most comfortable of things to talk about," said the 35-year-old former England captain.
"I think what we made clear to him, and what he already knows, is that, if we were to get the World Cup in our country in 2018, our media will be right behind it."
The International Olympic Committee has said it is to investigate BBC claims of corruption against Fifa vice-president Hayatou, who is also an IOC member.The IOC has also asked the BBC to hand over any evidence of alleged bribes taken by Fifa executives.
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