The Panelbase survey found 34% agreed the country should be independent, with 47% opposed.
The figures show those in favour of Scotland leaving the UK has fallen by 3% since October, with those voting to remain in the union up 2%.
However, those who have still to make up their minds also increased by 2% to 19%.
The poll also put some of the claims arising from the independence debate to voters, including the country's status in the EU.
It found 60% of the 800 respondents agreed an independent Scotland would not automatically become a member of the European Union.
One third said they would be less likely to vote yes if Scotland did not automatically become an EU member.