Nationalists believe an independent Scotland would have no problem remaining in the European Union.
Barroso has said any country winning independence from a current EU member state would have to renegotiate its membership.
“In the hypothetical event of a secession of a part of an EU member state, the solution would have to be found and negotiated within the international legal order,” he said in recent remarks.
Unionist politicians jumped on the statement, which they said meant an independent Scotland risked losing EU membership.
David Martin, a Labour MEP and the party's spokesman on constitutional affairs, said membership was not automatic.
"An independent Scotland's membership of the EU is far from clear, and there is no precedent to suggest membership would be automatic," Martin said.
“President Barroso’s recent comment reflects what the European Commission has been saying for a long time," he said, adding that the situation is "certainly not as clear-cut as the SNP would like to believe."
Martin added the European Commission, the European Parliament and all member states would have to agree to Scotland becoming a new member.
A Scottish flag in Brussels
But the Scottish Government have said there is nothing in Barroso’s response that suggests Scotland will not retain its place in the EU.
SNP MEP Alyn Smith said unionist parties were scare-mongering.
“The president has made it clear he is not going to get involved in these discussions because this is a matter for the people of Scotland. It is utterly inconceivable this could be any other way," Smith said. “Membership is a formality and the people of Scotland will decide.”
European Commission spokesman Olivier Bailly said today (11 September) that an independent Scotland would be left outside the union, at least temporarily.
“Any secession process for member states will have to be organised according to international law so that this new organisation gets recognition from the international community,” Bailly said.
“Then if they want to apply for EU membership this will have to be done by treaty regarding provision for accession.”
But he added, “All that is speculative and we have not received any request so far.”