It represents the latest stage in a process that will end with the announcement of Stuart Pearce's final 18-man squad on July 6.
There has been a huge amount of debate around who will be the three overage players in Pearce's squad.
Ryan Giggs, Craig Bellamy, Rio Ferdinand and Frank Lampard have all been mentioned as potential candidates.
Beckham's name has been a constant, though, mainly due to the influential role he played in getting the Olympics to London in the first place.
The 37-year-old's popularity remains undimmed, even though he has not played his club football in England for nine years now.
He was greeted with rapturous applause at Wembley on Saturday when given a special award for reaching 100 caps by UEFA, and it is believed the former Manchester United midfielder remains amongst the players Pearce has submitted.
There is little doubt Beckham's presence would help sell tickets for the football event, which features Great Britain's group matches at Old Trafford, Wembley and the Millennium Stadium.
It is yet to be decided whether the FA will formally announce the 35-man squad.
However, it is also believed young goalkeeper Jack Butland remains in the squad.
Although they had previously stated no player who was selected for Euro 2012 would be involved in the Olympics, it is thought Pearce would be willing to bend the rules for Butland, who has been elevated to England's third-choice keeper.
Butland has expressed a desire to remain in Olympic contention, although club side Birmingham would have to sanction the move.
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