The European Commission (EC), the EU`s governing body, has made clear it will only comment on an independent Scotland`s prospective EU status if it is approached by a current EU member state.
The pro-independence Scottish Government is not entitled to seek its own opinion as it is a devolved administration within the UK.
Only the unionist UK Government is permitted to approach the EC, but has made clear it will not "pre-negotiate" the terms of independence ahead of the referendum.
SNP MEP Alyn Smith has written a letter to Prime Minister David Cameron, Scottish Secretary Michael Moore and Deputy First Minister Nicola Sturgeon urging them to make a joint approach to the EC.
He urged Tory MEP Struan Stevenson, Labour MEP Catherine Stihler and Liberal Democrat MSP Liam McArthur to add their names to the letter at a European hustings-style debate at Edinburgh University this evening.
It states: "As four politicians elected in Scotland from four different parties, we believe that the best way for the Scottish and UK governments to secure EC opinion specifically about Scotland's membership of the EU as an independent country is for the UK Government, as the existing member state, to formally seek such an opinion.
"In line with a key recommendation of the Electoral Commission, which calls on the two governments to agree a `joint position` on the consequences of both a Yes and No result `so that voters have access to agreed information about what would follow the referendum`, we urge the Scottish and UK governments to agree an approach to the EC on the question of EU membership."
None of the MEPs indicated whether they would sign Mr Smith's letter at the debate tonight.
Mr McArthur echoed the comments of his Liberal Democrat colleague Michael Moore, saying the SNP is "trying to hang a picture that has not been painted".
Mr Smith insisted he was not looking for an answer tonight, and left it open for his MEP counterparts to sign the letter once they have had time to consider its contents.
Ms Stihler criticised the Scottish Government for taking the Information Commissioner to court to challenge her freedom of information request for legal advice on Europe, which it later transpired did not exist.
Mr Smith admitted that the decision "put us in a very unfortunate position".
He said: "It was the best letter that Catherine ever wrote and it was a very fair question.
"In our defence, it is a convention across all governments worldwide that the existence of legal advice is not admitted to one way or another.
"The UK Foreign and Commonwealth Office has done the exact same thing over the existence of its legal advice, and you'll be hearing more about that in the weeks to come."
Ms Stihler also likened an independent Scotland to the fictional Denmark in popular political drama Borgen, where the Danish European Commissioner is responsible for multilingualism.
"That's all Denmark gets," she said. "If you look at that and look at what it means to be a small member state compared to what we have as a big member state, having the foreign affairs brief, creating the diplomatic service in the EU - size does matter."
Mr Smith responded: "Borgen is fictional. The actual Danish Commissioner is Connie Hedegaard whose responsible for the EU's efforts against climate change, which is a very significant portfolio."
He criticised Mr Cameron's plan for an in/out referendum on Europe, arguing that it would not head off the threat to the Conservative vote by anti-Europe party Ukip but "feed red meat to the beast".
"In exactly the same way as John Major and Margaret Thatcher were scuppered by Europe, he's brought up an issue which is not of immediate relevance to the vast majority of people and the Tories are going to obsess about it for years to come."
Mr Stevenson argued that Mr Cameron was right to seek a good deal for Britain in the EU in the face of eurozone reform "which will actually mean Brussels under the diktat of Berlin".
He also called for a renewal of the opt out of the EU social chapter, which provides common working conditions for EU citizens.
"Why is the Westminster Government or Holyrood not responsible for the working conditions of UK people?" he said.
"We elect MSPs and MPs, they should be the ones that say what the working conditions should be for our workers. Right now it's Brussels that says how many hours our junior doctors should work, and there is now a big debate about whether there should be women represented on corporate boards.
"We're in the middle of a eurozone crisis and we're having debates like this adding more red tape and more bureaucracy."
Commenting on the response to his letter, Mr Smith said: "I challenged my MEP colleagues and Liam McArthur tonight so that this important information is available to Scots to have before we vote for independence in autumn 2014.
"I think that the Scottish and UK governments are well placed to ensure, through joint working, that a sensible and considered request goes to the European Commission.
"I strongly urge the anti-independence parties to settle this verbal ping-pong and urge the two governments to work together in the best interests of the Scottish people and obtain this Commission opinion.
"The letter urges co-operative action between the Scottish and UK governments to seek EU clarification just as the Electoral Commission has urged."