The UK Government source said: “All these countries have problems with separatist groups themselves and they have made it clear that they do not want to provide them with any encouragement by accepting Scotland into the EU.
“On top of those four, Hungary has also let it be known they might also veto Scotland.”
The UK Government also insists the legal position is an independent Scotland would have to apply as a new member.
While some senior figures in Brussels have been warm about Scottish membership the source added: “In the end they can quote some comment they may have head in a Brussels cafe but the hard realities of the EU are that it takes 27 countries to each agree a new member.”
SNP Brexit minister Mike Russell dismissed Mr Mundell’s speech as “ridiculous”.
He said: “Just a few months ago Mr Mundell, Ruth Davidson and many other Tories warned us of the disastrous consequences of leaving the EU – yet now they try and pretend that the UK offers some sort of stability or certainty for Scotland.”
A Scottish Government source added: “We are not proposing to leave the EU – the people of Scotland voted overwhelmingly to Remain, and we are doing everything we can to protect Scotland’s place in and relationship with the EU.
“Given the complete mess the UK Government has made of the EU referendum result and their relationship with the European Union, perhaps they should focus on improving their own relationships with EU governments rather than running around desperately trying to smear Scotland’s reputation abroad.”