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Euro 2012, jointly hosted by Ukraine and Poland, will be the last to feature 16 teams after UEFA voted last year to expand the tournament to 24.
"The infrastructure required for the new expanded tournament makes it extremely difficult for us to even consider hosting," SFA chief executive Gordon Smith said.
"Quite apart from the stadia required, the pressure on transport, training camps and accommodation would be massive."
"We do want to host a major championships here in Scotland but, particularly in these tough economic times, we have to be realistic about the huge costs involved.
"Our focus for now is on qualifying for the big events in our own right."
Football Association of Wales (FAW) secretary general David Collins said: "The current economic downturn and the very considerable implications for infrastructure provision following UEFA's decision to expand the finals are key considerations.
"While the ambition to host a future tournament remains undiminished the unanimous view is that a bid for Euro 2016 is premature and will not maximise Scotland and Wales' chances of success.
Deputy first minister and minister for economy and transport, Ieuan Wyn Jones said: "In Wales, only the Millennium stadium meets UEFA's tournament requirements and the cost of bringing other venues up to this standard would run into tens of millions of pounds.
"In the current economic and financial climate this is unaffordable."