Scotland has never hosted a major football tournament
Scotland could be the beneficiaries if Uefa takes a dim view on Ukraine and Poland's preparations for Euro 2012.
Doubts persist about the suitability of stadiums and infrastructure in the former Eastern bloc nations and an inspection is planned this summer.
SFA chief executive Gordon Smith told BBC Sport: "We have made it clear that we'd like to be considered if it's not going ahead in Ukraine and Poland.
"With the event likely to expand after 2012 it would be our last chance."
Scotland and the Republic of Ireland failed with a joint bid for Euro 2008, which gets underway in Switzerland and Austria at the weekend.
But Smith revealed that he had held discussions with Uefa president Michel Platini about hosting future tournaments.
People here feel there are too many problems to host this tournament
Igor Miroshnychenko, Ukraine FA
"I asked if the size of the competition was increasing from 16 teams," he said.
"And, given that it probably would after 2012, we would not be able to stage a European Championship if that was the case.
"But he (Platini) said there might be an opportunity, you never know.
"There is an inspection on Ukraine and Poland's facilities in June or July and if they don't match up they may have to take the tournament elsewhere.
"I said was that we'd like to be considered if that situation arose. We haven't been told we are on standby or anything like that."
Igor Miroshnychenko from the Ukranian FA told BBC Sport: "I have heard the story about the possibility of the championships being taken off us.
"I spoke with Uefa on Wednesday and they told me that they have no plans at the moment to move elsewhere.
"But it's not a good situation here at the moment.
"We have no main stadium and there are problems with the roads. It's not a good situation politically.
"People here feel there are too many problems to host this tournament. Can we host it? I really don't know."
Italy was widely expected to win the Uefa vote for Euro 2012.
However, their bid was overshadowed by a referee corruption scandal and problems with football-related crowd trouble.
Scotland's First Minister Alex Salmond is a keen football fan and has voiced his interest in the nation hosting a major event.
"I've had discussions with Alex Salmond and the Scottish government and they would like us to apply for a tournament," added Smith.
"We know about the criteria that has to be met and there is a financial cost to that, so we'd have to see if that money could be raised by government."
Hampden Park, Ibrox, Celtic Park and Murrayfield, the home of Scottish rugby, all meet international standards.
But another four stadiums would have to be constructed or upgraded in order for Scotland to succeed with any bid.