The First Minister shocked the UK Government with her announcement on Monday that she wants a second independence referendum to be held between autumn 2018 and spring 2019.
She said it would be a "defining moment" for Britain.
Scots rejected independence by 55-45 per cent in a referendum in September 2014.
The EU's Stability and Growth Pact ensures that new member states are expected to have a budget deficit of just 3% of GDP.
But Mr Brown said: "It may come as a surprise to some people but trading with your nearest neighbour is the norm the world over, but the inconvenient fact for our opponents is that these countries who trade with their neighbours are in fact independent countries".
"She is the person threatening a second independence referendum, yet she refuses to give voters the clarity they need".
He said: "If the Scottish Parliament decides that there should be a referendum after the Brexit negotiations are concluded, but before Scotland is dragged out of the European Union, will she respect that?"
She added: "It's really important to be in the single market".
In an interview on ITV's Peston on Sunday programme, Miss Sturgeon admitted there may be "room for discussions" about the timing of the proposed referendum.
Wales - together with England - voted in favour of leaving the European Union, while Scotland and Northern Ireland opted to remain.
Scottish government oil sector tax receipts amounted to just £60mn in Fiscal Year 2015/16 if oil revenues are shared on a geographical basis as the Scottish government argues they should be.
But Sturgeon, undeterred, plans to ask the Scottish Parliament next week to start the process of seeking a new referendum.
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JBS also said the employee questioned in this matter played no strategic role in product quality or any verification processes. BRF said in an emailed statement that he surrendered to the authorities and is available to give all clarifications needed.
Earlier, Ms Sturgeon told Sky News' Sophy Ridge on Sunday that Scotland would seek to remain part of the European Union.
"All our energies should be focused on our negotiations with the European Union", May said, adding that holding a Scotland referendum while EU exit talks were still under way would "make it more hard for us to get the right deal for Scotland and the right deal for the UK".
At the same time Scotland would also find itself outside North Atlantic Treaty Organisation, the main Western alliance.
"In 2014, when I was arguing the case for independence, the United Kingdom was very firmly in the EU", Sturgeon said.
She told the SNP spring conference in Aberdeen that one medic, who had spent more than 25 years working for the health service in Scotland, had been left feeling he "was no more than a pawn in Theresa May's Brexit game".
"It is for (May) then to say what timescale she thinks would be appropriate and then yes I am happy to have that discussion within reason", Sturgeon told the British broadcaster.
May has said she will not agree to any referendum taking place before Brexit, telling Sturgeon "now is not the time" for the vote to be re-run.
Closing the SNP conference, Ms Sturgeon will say: "We know change is coming".
A recent YouGov poll also showed that even if another vote was held, 57 percent of Scots would reject independence yet again.
Mundell said there would be no negotiations on Section 30, a procedure that allows the Scottish parliament to legislate for an independence referendum.
"We should be working together to get that right deal for Scotland, that right deal for the UK". There would be an independence referendum, but possibly not before the Brexit process was completed in 2020.
"To do so now, while all our energies should be directed towards the negotiations with Europe, would make it more hard to get the right deal for Scotland and the right deal for the United Kingdom as a whole".