The poll, which was commissioned by the Labour Party showed that retaining the pound was the strongest preference for more than two-thirds of voters.
The data also revealed that Brexit is considered to be the most important issue facing those living in Scotland today with the NHS, immigration and the cost of living following after.
Scottish independence was ranked as the most important by 8% of people with the majority of “Yes/Remain” voters said Brexit was more important than independence.
The poll also found that 36% of respondents who voted SNP in 2015 agreed with the statement that the party should “stop talking about referendums and get on with the job of governing Scotland”.
Over 30% of SNP supporters backed Brexit last year with a divide on European and independence issues among Yes voters.
Dave Anderson, Labour’s shadow Scottish secretary, said: “This polling makes clear the SNP does not even speak for its base support let alone the whole of Scotland.
“It is clear that Scots don’t want a hard border with the rest of the UK and neither do they want to join the euro, both of which would almost certainly become a very real prospect if the SNP got its way and Scotland left the UK and joined the EU.
“The SNP are about one thing and one thing only. But, as this polling shows, their latest strategy to use Brexit to help with their cause of independence is not something the Scottish people will support.”
One of the polls asked respondents about the possibility of hard borders in the UK saying “If the rest of the UK left the EU but Scotland remained in, there could be a ‘hard border’ (i.e. border checkpoints) between Scotland and the rest of the UK. If you had to choose, what would you rather have?”
61% backed free trade and no borders with the rest of the UK but with Scotland outside of the EU.
39% preferred hard borders with the rest of the UK but with Scotland in the EU.