Blatter was in Belfast for a meeting with the four home nations
Fifa has warned that a unified British Olympic team would jeopardise the independence of the four home nations, according to the Scottish FA.
SFA president George Peat claims his Fifa counterpart Sepp Blatter now admits a Team GB would pose a risk.
"Mr Blatter told us at an informal function that, if we agreed to be part of Team GB, our position would be in jeopardy," said Peat.
Scottish, Welsh and Irish associations oppose a British team for London 2012.
And, before this weekend's International Football Association board meeting in Belfast, Blatter was quoted on news wires as suggesting that it was the Celtic nations' very opposition to the idea of a British team that could put their independence at risk.
But Peat believes the SFA's strong stance has been vindicated by comments he claims the Fifa president made in private.
"My immediate reaction was one of surprise," he said. "I glanced over at the English table and their two guys, Lord Triesman and Sir David Richards, just looked at each other."
As the team is not identified as a Scottish or Welsh or Northern Ireland team then, if players should like to play for it, we should not forbid them to play in the Olympic Games
Fifa president Sepp Blatter
Peat reiterated that Scotland's representatives at the top tables of world and European football - a former Fifa vice-president and the current Uefa general secretary - had also warned against taking part.
"David Will, who was Fifa vice-president for 15 years, has always told us on no account to get involved," he said.
"David Taylor says the same thing. So we're viewing this as a serious warning."
The SFA recently wrote to the British Olympic Committee outlining their opposition to a Team GB in a joint letter with their colleagues in Belfast and Cardiff.
Peat insists there will be no going back on their decision despite lobbying from the UK Government - including Prime Minister Gordon Brown, himself a Scot - and the FA chairman.
"Lord Triesman has told us we've upset the Olympic committee with our letter, but that doesn't make any difference to us or our stance on the issue," he said.
Asked by the Press Association if a Team GB would jeopardise the status of the four British associations, Blatter had earlier replied: "In principle, I would say not.
"Let them make a team and if Scotland don't want to play then don't play.
"But the more noise you make, the more people in Fifa will be alarmed."
Blatter also warned that no British player should be prevented from playing in the 2012 Olympics.
"Unless the IOC will expel football from the Olympic Games, there will be a Great Britain football team at the London 2012 Games," he said.
"As the team is not identified as a Scottish or Welsh or Northern Ireland team then, if players should like to play for it, we should not forbid them to play in the Olympic Games."
An FA spokesman said there was no change to its continued support for a 2012 British team, the composition of which will be decided by the BOC.
The English association would prefer a team open to players from all four home nations but is prepared to supply the whole squad if necessary.
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