More than one in five Scots who say they plan to vote have yet to decide which way, the TNS survey found.
Pressed on which side would likely win their support almost a fifth, 19%, said Yes, while 15% said No.
Two-thirds, however, still insisted they could not decide.
A separate poll of 1090 adults also showed increasing support in England and Wales for Scotland to remain part of the UK, following a concerted campaign by the UK Government to "lovebomb" the Scots. It showed 61% believe Scotland should not be a separate country, up eight percentage points since August.
Overall, however, the TNS poll of 1011 Scots aged 16 and over found voting intentions unchanged from the previous month, with support for No at 42%, for Yes at 30% and undecided 28%.
But among those certain to vote support for independence dipped slightly, by one percentage point to 34%, with more people becoming undecided and support for the Union unchanged at 44%.
Better Together downplayed the significance of more "don't knows" choosing Yes than No, pointing to the small sample size.
The No camp also said the SNP's "claims of momentum are difficult to take seriously" with polling numbers unchanged.
But Yes Scotland hailed the finding that undecided voters were more likely to back them.
At the weekend Yes Scotland claimed "don't knows" were moving to Yes at a rate of seven voters for every three who backed No.
Both sides welcomed the results of the poll, which was carried out before the recent row over whether Scots would be £1000 better off or £1400 worse off following independence.
Blair Jenkins, Yes Scotland's chief executive, said: "This is a very welcome poll - of those certain to vote, excluding undecideds, Yes now sits at 44%, which is eight points up on last autumn, and within reach of the winning post in September."
Better Together campaign director Blair McDougall said: "It is encouraging that yet another poll shows the campaign to keep Scotland in the UK with a strong lead."
Meanwhile, German Chancellor Angela Merkel refused to get involved in the debate yesterday. At a press conference with David Cameron in Sweden, she dodged a question on whether or not an independent Scotland would be part of the European Union. She said she did not answer hypothetical questions.