Ska Keller, co-president of the Green bloc of MEPs at the European Parliament, said there was a widespread sympathy in Brussels with Scotland's position given that a majority of Scots had voted Remain at the 2016 referendum.
Ms Keller, who served in regional German government before being elected to Brussels, was speaking as a guest of the Scottish Greens in Glasgow today.
She added that Scotland also meets the criteria to permit re-admission - rubbishing claims the country's deficit would hinder accession to the EU.
"I can't speak for other groups or parties, but for us Greens it's a very important thing. Obviously it's up to the people of Scotland to decide on their future.
"The only thing we're saying is that we would do everything we can to allow for a swift return.
"Scotland fulfils all the normal accession criteria, has all the European rules and regulations, so there is really no need for lengthy discussions and negotiations.
"This is a case of a country wanting to rejoin and I think it would be politically so stupid to then close the doors of that, and I hope that all the member states will see that - and I'm also quite confident that they will see that."
She maintained Scotland would be able to get back into the EU despite its current seven per cent deficit, adding: "There are so many countries who have so much of a deficit who are inside and that's not a problem."
Opponents of independence have said accession to the European Union would only be granted to nations which have a deficit of 3% or lower.
But Ms Keller said this is only for access to the European currency, which First Minister Nicola Sturgeon has said she would not seek to use.
Ms Keller said there is "a lot of sympathy" among European countries for Scotland - where 62 per cent of people voted to remain in the EU in 2016.
She added that sympathy would have to translate into "political action" for Scotland to be welcomed back into the EU.