Umberto Gandini, vice-president of the European Club Association (ECA), said UEFA should pressure member associations and national team managers not to select the same player for both tournaments.
"We do not think it is appropriate that European players will play in the European championship and then some of the same players will be involved in the Olympics in London a few weeks later," Gandini told a news conference.
"It does not make sense for a club player to be involved in two major tournaments in such a short period of time. We have appealed to UEFA to say that if a player is selected for Euro 2012, he should not be selected for the Olympics.
"As the Olympics are not part of the international calendar we are going to face the same situation we did in 2008 where there will be requests for release of players where the clubs have other activities going on.
"We hope we can discuss this without getting into conflict as we did in 2008."
Manchester United chief executive David Gill, speaking in his role as an ECA board member, said the debate was part of a wider concern that clubs did not want their players taking part in more than one international tournament a year.
Gill said the clubs would prefer their players to miss the Olympics, which starts four weeks after Euro 2012 ends.
"A player who is in the squad for Euro 2012 should not then be in the Olympic squad," he told the press conference.
"Football is a key part of the Olympics and we are very happy to participate as a League and release players, and we support it, it will happen - but I hope that common sense will prevail."
Four European teams will take part in the 16-team men's Olympic tournament, which is being staged around Britain, with nine events taking place at United's Old Trafford stadium.
Unlike the European championship and World Cup, a British team will enter the Olympics rather than teams from England, Scotland, Wales and Northern Ireland, and there has already been much debate about the composition of that team.
The Football Associations of Wales, Scotland and Northern Ireland are reluctant to release their players for the British team in case it compromises their individual memberships of FIFA.
Olympic teams are Under-23 in nature, with three over-age players allowed to take part.
The British team, as hosts, are the only certain European qualifiers to date with the three other finalists coming from the top three finishers at the European Under-21 championships in Denmark later this year.
