The Manchester United midfielder was not among the players written to by the Football Association before Christmas because he had not then come out of retirement and was not registered as a player.
However the 37-year-old could still be considered as a contender for one of three over-age places in Stuart Pearce's squad - the remainder will be made up of under-23 players.
If Scholes wishes to be considered he would have to contact the FA to make himself available, or Pearce could approach the United player himself.
Fellow thirtysomethings David Beckham and Ryan Giggs are among 184 of 191 players who have indicated they wish to be considered for the Olympics men's team.
Pearce will not pick any player for the Olympics who has been part of Fabio Capello's squad for Euro 2012 which means there is a greater chance that Giggs, 38, or 36-year-old Beckham, or indeed Scholes, could feature.
The seven players who ruled themselves out are from across the home nations, including at least one Englishman, and from a spread of clubs. British Olympic Association communications director Darryl Seibel said they were delighted with the response.
Seibel: "This is an outstanding response and it confirms what we have believed all along, which is there is widespread interest among players in competing for Team GB at the London 2012 Games.
"Clearly, the players recognise just how special this opportunity is."
Players who wanted to be in the Team GB Player Pool, from which coach Pearce will pick his squad for the Olympics, did not need to provide a written response to the FA. However, a large percentage of the 184 players did contact the FA to confirm they wanted to be considered.