Pearce has travelled to California to watch Beckham in action for the Los Angeles Galaxy but BOA chief Andy Hunt says there has never been any suggestion to the Olympic coach to choose the 37-year-old in order to sprinkle some stardust on the squad.
The men's Olympic squads are restricted to players aged under 23 but three over-age players are also permitted.
Hunt said: "Stuart Pearce will make a decision on the best squad available given where he is in respect of now having assessed the players that are not involved in the Euros and the current state of injuries.
"He will then make the best call he can - on merit.
"I am not putting any pressure of him whatsoever to pick anyone. We discussed the whole topic of selecting over-23 players back more than a year ago but I haven't subsequently.
"We have been very clear from the outset, it's absolutely Stuart's choice and he is totally free to make the selection of the team he believes will put in the best performance. It's as simple as that."
The Football Association have agreed that any player involved Euro 2012 with England will not be selected for the Olympics as well.
Pearce is expected to name his squad at the end of next week. Manchester United have already indicated they do not want any over-age player - such as Rio Ferdinand - to be considered apart from Ryan Giggs.
Opposition to the British team remains from the other home nations apart from England but a number of players such as Wales duo Aaron Ramsey and Gareth Bale have already stated their desire to be considered.
Hunt said that for some players the Olympics would be their only chance to appear in a major tournament finals.
He said: "For those who are unlikely to play at the highest international level for their country - well here's a chance."
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