The Herald revealed yesterday the Latvian Prime Minister, Valdis Dombrovskis, has invited ministers to Riga.
The country is to hold the presidency of the Council of Europe in 2015 and would direct the EU's response to any bid for membership.
However, Mr Dombrovskis said an independent Scotland could not expect to inherit the UK's terms.
Scottish Labour MEP Catherine Stihler said: "Scotland would lose all the opt-outs we have as part of the UK, lose the rebate and have to join the euro. If the SNP want to dispute that, why not take up Prime Minister Dombrovskis's offer?"
A Scottish Government spokeswoman said: "We are happy to discuss Scotland's future as a constructive independent member of the EU with our European partners, and we look forward to further such discussions.
"It is possible to prepare a scenario that will provide the European Commission with the information it needs to consider an independent Scotland's continued EU membership, and we call on the UK Government to join us in making such a submission."