But opposition to a rerun of the 2014 plebiscite has hardened, with the number of Scots against such a vote rising six points from June to September.
Polling shows 46 per cent against another referendum, while 33 per cent believe one should be held in the next two-to-three years, while the UK is negotiating to leave the EU, according to a poll tracker by What Scotland Thinks.
A further 21 per cent believe a second vote should happen - but only when Brexit has been concluded.
“Those who are opposed to independence certainly do not want another referendum, while those who are in favour are relatively inclined to want to hold one, although some of the polling that asks when it should take place shows disagreement on a date,” said John Curtice, professor of politics at Strathclyde University and chief commentator on What Scotland Thinks.
“But apart from timing subtleties, it’s almost inevitably the case that what you get when you ask people about a second referendum, their answer is determined by how they voted the first time.
“There’s no sense of malaise among Yes supporters - another referendum is their only chance of realising what they are in favour of.
“If you don’t want independence, you don’t want a referendum on it - you’re quite happy with the status quo. Unionists will get fed up with the debate continuing.
“But irrespective of Brexit, and what Nicola Sturgeon is or isn’t going to do, the referendum left Scotland divided down the middle on the subject and therefore the debate is continuing.”
The Scottish independence debate was reignited by the Brexit vote in June, in which a majority of voters across the UK backed the country leaving the EU - despite Scots supporting continued membership by 62 per cent to 38 against.
Nicola Sturgeon said in a keynote speech in July that independence may offer the most “certainty and stability” for Scotland if the UK opts to quit the European Union, as expected.
The Scottish Conservatives have in turn claimed the SNP is merely looking for a “flimsy excuse” for another independence campaign.
Jackson Carlaw, deputy leader of the Scottish Conservatives, said: “Time and again polls have proved that Scots don’t want to be dragged back into another divisive referendum on independence.
“We settled this issue decisively in 2014 and people want to move forward. It’s now time that the SNP listened to Scots instead of dragging us back to arguments of the past.”
An SNP spokesman said: “Scotland voted overwhelmingly to remain in the EU, and the Scottish Government is exploring all options to protect our place in Europe – including the option of an independence referendum if it becomes clear that this is the best or only way to protect Scotland’s interests.”