The Scottish, Welsh and Northern Ireland Football Associations have been united in condemning the British Olympic Association's statement which suggested players from each of the home nations would be eligible for Team GB.
Scottish Football Association chief executive Stewart Regan denied any agreement had been reached with the BOA and reiterated his belief such a move would be a threat to the autonomy of his organisation, a view backed up by former Scotland boss Craig Brown.
However, Butcher believes the opportunity for players to take part in the Olympics should be grasped.
"If it's good enough for the athletes to be in Team GB, from any nationality, then it should be good enough for the footballers," the former England skipper told STV.
"My view is that we should have a united Great Britain team that represents Great Britain in football.
"I'm disappointed that some countries have taken a stance against it, very disappointed about that, because if it's good enough for the athletes it's good enough for the footballers."
Aberdeen boss Brown, however, believes the current lack of trust in FIFA is a very good reason to avoid the creation of a Great Britain football team.
"It's quite a harsh thing to say but I do think there is a lack of trust in the FIFA organisation," Brown told Talksport.
"Over the years there has been suspicion of the motives of FIFA and of course they would like to have one vote for Britain instead of four votes.
"The main argument is that Scotland would lose its identity.
"I think the feelings are that FIFA are desperate to combine the home nations and make it a Great Britain team and there would be no separate England, Wales, Scotland or Northern Ireland teams.
"When this issue first arose a few years ago the late David Will, who was former president of the SFA and vice president of FIFA, wrote to me and I still have the letter.
"He more or less said you could trust FIFA at the moment but successive committees and maybe a new president eventually, could change the whole thing, so it wouldn't be a binding commitment, it would be a temporary one."