The EC's top official will not respond to the Deputy First Minister's request for several days as he weighs up the request, commission sources said.
Brussels regards the request for talks by the Scottish Government as "political" and is wary of being drawn more deeply into a row over Scottish independence.
In a letter on Monday, Ms Sturgeon called for urgent talks with President Barroso after declaring he was wrong to suggest a newly independent Scotland would have to apply for EU membership and negotiate conditions with other members states.
She is seeking face-to-face talks to press the SNP's claim that an independent Scotland would remain in the EU and inherit crucial UK opt-out on the euro single currency and Schengen free travel area, which has ended border controls in much of Europe.
Mark Gray, a spokesman for President Barroso, said: "The President has made clear throughout he was not dealing with a specific situation, be that Scotland or Catalonia or anywhere else."
However an EC source said: "Holding talks would be a political question in itself, we cannot pre-empt his decision."