England Under-21 coach Stuart Pearce was named on Thursday as the coach of the British team at next year's London Games and while he will select mainly Under-23 players, the rules allow for three over-age players to be included.
The English FA, operating the British team under the auspices of the British Olympic Association (BOA), said on Thursday that Pearce could pick any eligible players for his squad, and while it is doubtful that any players involved in the European Championships would also play in the Olympics, it remains a remote possibility.
Bevington commented: "We are aware of the challenges that playing in the Euros and the Olympics would present to any player, but we are not going to lock ourselves into a situation where we say if you go to one, you can't go to another."
"At no time during Thursday's media conference to announce the Team GB Olympic Coaches did The FA representatives at any stage suggest or propose the names of Wayne Rooney, any Manchester United player or Jack Wilshere as possible members in the Olympics squad," a statement said.
"Furthermore, The FA did not say players would be selected for both tournaments, but stated clearly the organisation would not be locked into a policy of ruling it out.
"We also made it very clear the need for sensible dialogue with clubs, players and representatives and that everything would be handled with common sense."
Other United players, who do not play for England, could be called up to the British Olympic team which would put a strain on United's pre-season preparations.
They include Scotland's Darren Fletcher, Northern Ireland's Jonny Evans and Welsh veteran Ryan Giggs, even though the Wales, Northern Ireland and Scotland FAs have all said they do not want their players involved in the British team as they fear it will compromise their independent status within FIFA.
Ferguson told reporters on Friday: "This is spurred by Argentina in the last Olympics, and Nigeria, playing their strongest teams, that's where it's come from."
"It's given the British Olympic team an opening to start thinking in the same way.
"But we have a different type of football to abroad, as everyo
