The first TNS poll of 2016 found that 44 per cent of voters would opt to remain a member of the EU, while 21 per cent would vote to leave.
In May last year, 49 per cent of voters would have opted to stay in, which fell slightly to 47 per cent in September last year.
Meanwhile, 19 per cent of Scots would have voted to leave the EU in May last year, which fell slightly in September to 18 per cent, before rising to 21 per cent now.
However, 29 per cent of voters said they did now know how they would vote.
"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," Tom Costley, head of TNS Scotland said.
"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," he added.
The results are particularly problematic as First Minister Nicola Sturgeon has already indicated she would be very likely to regard the UK voting to leave the EU, but Scotland voting to remain, as a "trigger" justifying a second referendum.