Two surveys suggest there will be a victory for the Better Together campaign, but that undecided voters could narrow the gap.
Support for independence stands at 37% while backing for the union is 47%, according to a Panelbase survey of 1,002 adults
The poll, commissioned by The Sunday Times and Real Radio Scotland, suggests 16% are undecided.
Among those certain to vote, support stands at 44% for independence and 56% for the union.
When the undecided group were asked if they had pick a side today, the gap shrinks, putting Yes at 47% and No at 53%.
A separate poll conducted by ICM for the Scotland on Sunday newspaper gave the No camp a stronger lead.
It puts support for independence at 32% and support for the union at 49%, while 19% do not know.
Among people certain to vote, support for independence is 40% compared to 60% backing the union.
But the lead narrows to just 10 points when people are asked to assume a No vote would not guarantee extra devolved powers for Holyrood.
The results are evidence that the momentum is with the independence movement, according to Yes Scotland chief executive Blair Jenkins.
He said: "When people consider the consequences of a No vote next year, support for Yes increases. We already know that people are more likely to vote Yes if they think there will be another Tory government or the UK will leave the EU."
Deputy First Minister Nicola Sturgeon said: "Polls will move up and down between now and next September, but these encouraging figures show that more people are choosing good government with independence rather than bad government from Westminster."