The Sunday Mirror says Princes William and Harry are hosting a reception, in aid of England's 2018 World Cup bid, in Johannesburg on Saturday.
Organisers have asked England manager Fabio Capello to give Beckham special permission to attend.
The timing, the afternoon after England's second group game, against Algeria in Cape Town, is far from ideal.
But Beckham, figurehead of the bid team, is keen to play a role.
An insider revealed: "This is an important showcase for us.
"The Princes are keen football fans, who are happy to do what they can to help the bid.
"We hope David will be able to join them."