A new TNS poll of 1,016 adults in Scotland found 44% would vote to remain in the EU in the forthcoming in/out referendum, down from 49% in May and 47% in September.
Support for a leave vote has risen to about one in five (21%) from 19% in May and 18% in September.
The poll, carried out between January 6 and 25, found almost a third of voters (29%) remain undecided about how they will cast their vote.
Tom Costley, head of TNS Scotland, said: “With the referendum on membership of the EU looking increasingly likely to take place in 2016, people may be starting to focus on Britain’s membership of the European Union despite concerns expressed by the First Minister about holding the referendum in June so soon after elections to the devolved assemblies.
“With such a high level of ‘don’t knows’ it’s still all to play for, and there remains a positive view of the European Union in Scotland.”
On voting intentions for May’s Holyrood elections, the poll put support for the SNP in the constituency vote at 57% among those who expressed a preference and were certain to vote.
Labour support was at 21%, the Conservatives 17%, Liberal Democrats 3% and others 2%.
Backing for the SNP remained high in the regional vote at 52%, with Labour on 19%, the Conservatives on 17%, Liberal Democrats 6% and Greens 6%.
The poll also recorded an increase in the percentage of people saying they are certain to vote, up to 65% from 58% in December.