According to the Daily Mail, Mel B, Mel C, Emma Bunton and Geri Halliwell are still interested in playing the show on August 12.
"They would have a few weeks to rehearse," a source told the newspaper.
"This is a serious proposition, Mel B has been bombarding Victoria with calls - she's the sticking point. All the other girls want to do it. Victoria is extremely reluctant."
All five Spice Girls reunited earlier this week to launch the Viva Forever! musical which features their hit songs.
The launch marked the first time all five women were together in public since their ill-fated 2008 reunion tour.
Earlier this month after a playlist of songs for the ceremonies was leaked, Mel C admitted that she would be "really upset" if the group were not included in any form during "the opening or closing ceremonies or any other playlists".
In 2010, the singer started a campaign for the group to perform at the London 2012 Olympics and Mel B more recently said that a performance was a possibility.
It was suggested that the group would reunite for this month's Diamond Jubilee celebrations, but Beckham's reluctance to rejoin the band was the apparent stumbling block.
Spice Girls through the years - photo gallery:
Copyright: Rex Features