In a letter on his behalf, Vice-President Maros Sefcovic said the president could not "usefully discuss this further" without a "precise scenario" for Scotland leaving the UK.
Ms Sturgeon wrote to Mr Barroso in December after he told the BBC an independent Scotland would have to apply for European Union membership and re-negotiate its terms of membership.
The snub came as the former top civil servant in the Foreign Office warned an independent Scotland would face a "Herculean diplomatic task" to secure its share of the UK's £3 billion cash rebate.
Lord Kerr, an Independent peer, warned of a more "complex and costly" membership process than the SNP claimed, resulting in Scots paying more than the English to be in the EU.
In his letter, Mr Sefcovic stressed the EC had not commented specifically on the implications of Scottish independence but would offer a legal opinion if requested by the UK, as an EU member state. He added: "At the present stage, in the absence of a precise scenario, President Barroso has, therefore, asked me to signal he would not be in a position to usefully discuss this further with you."
Ms Sturgeon called on the UK Government to work with the Scottish Government to present a joint submission on steps towards independence for the EC to con-sider. She wrote in her referendum blog: "As I have said previously, it would be helpful if the UK and Scottish governments had discussions to develop a shared understanding of the issues on which we will require to negotiate after a 'yes' vote in 2014."
Scottish Secretary Michael Moore immediately dismissed the call, saying there was "nothing approaching a precise scenario" from the SNP.
He added: "It is up to the Scottish Government, not the UK Government, to do that work."
The SNP last year abandoned its long-held claim that an independent Scotland would automatically be an EU member on the same terms as the UK, including its cash rebate and opt-outs from the euro single currency and Schengen free travel area.
Ministers now accept negotiations would be required on all aspects of membership but insist talks would take place "from within" the organisation and Scotland could strike a good deal.
In a BBC HardTalk interview last December, Mr Barroso was asked whether Scotland's membership would be "nodded through". He said an independent country would have to re-negotiate terms.
Meanwhile, Lord Kerr warned an independent Scotland could face obstacles placed by Spain and other countries wishing to discourage their own independence movements.
Writing in political magazine Prospect, he suggested an independent Scotland would have to sign up to the euro in principle but, like Sweden, could avoid adopting the single currency in practice. However, he said it was "harder to see a happy outcome for Scotland" on budget talks, warning: "With no rebate, each Scot would pay considerably more than each Englishman."
He added: "Scots, especially Alex Salmond, must read the small print closely. They can't assume it would be easy or cheap to re-join the EU."
l Catalonia's Parliament has approved a declaration of sovereignty signalling the start of an uncertain journey towards a referendum on independence from Spain for the north-eastern region.