Mr Juncker's nomination to the EU's top job is expected to be confirmed in Brussels today, despite the outspoken opposition of Prime Minister David Cameron, who regards him as an obstacle to reform.
The former Luxembourg premier's appointment would break a decades-old tradition that the Commission chief is chosen by consensus of the EU's national heads of government, but Mr Cameron was left isolated in his opposition at the European Council.
SNP MEP Alyn Smith told BBC Radio: "From an SNP perspective we can do business with him.
"He has said sensible things about independence, not like his very unlamented predecessor.
"He has said that the independence process is entirely not a matter for the EU and the EU should respect any democratic vote.
"We can live with that, that's a sensible approach to take.
"We have not made our final decision on whether we will back him or not, but if he is the nominee I think we can do business with him."
Mr Juncker was prime minister of Luxembourg, which has a population roughly the size of Edinburgh, from 1995 to 2013.
South East England Conservative MEP Daniel Hannan rejected Mr Smith's portrayal of Mr Juncker as a pro-independence candidate, insisting that his appointment would lead to less sovereignty for all EU member states.
"This is a guy who believes in a European army, European police force, European taxation, common European citizenship," he told the same programme.
"I'm not sure Alyn is right to say that he believes in the independence of any country.
"Whether or not Scotland is in the UK, as long as Juncker gets his way in the EU none of the member states will be independent because we will be part of the United States of Europe."
Mr Smith described these comments as "hysterical".