Some 55% of people intend to vote No - up one percentage point on a similar poll in June - while support for independence has stood still at 35%, according to the YouGov poll for The Sun.
Support for independence rises to 39%, against 61% who say they will vote No, once undecided voters are excluded.
A majority of voters (61%) think Scotland should vote again if there is a No vote, against nearly two-fifths (39%) who say there should never be another vote on independence.
A quarter of people think the next vote should be held within 10 years, although the second largest proportion (17%) think Scotland should wait at least 20 to 30 years.
Independence is the most important issue facing Scotland, behind the economy, welfare and immigration, the poll of 1,142 Scottish adults aged 16 and over found.
Better Together campaign director Blair McDougall said: "Alex Salmond's failure to be honest with Scots about his Plan B on currency is costing him votes. It's clear that the momentum in this campaign is with those of us who believe the brightest future for Scotland is to remain part of the UK.
"Alex Salmond wants us to take a leap into the unknown with independence. He wants us to take a huge risk with the future of our country. Yet he can't tell us what money our wages, pensions and benefits would be paid in.
"He can't say what currency we would use to invest in our schools and hospitals. And he can't be clear about what money we would be paying our supermarket and energy bills in."
A Yes Scotland spokesman said: "This poll is unchanged from the last YouGov poll in June and two other polls in the past week have shown support for Yes as high as 47% - including the snap poll conducted after last week's debate.
"And a Yes vote is Scotland's one opportunity to protect the NHS from Westminster privatisation, create more jobs in Scotland, and transform childcare instead of wasting billions of pounds on Trident nuclear weapons."