A YouGov survey for The Sun and The Times found 52% of Scots are to vote for the union, with 48% favouring independence when undecided voters are excluded.
The result was mirrored in a Panelbase survey, which also found 52% of Scots back the union compared to 48% for independence, again when undecided voters are excluded.
A survey by Ipsos-Mori for the broadcaster STV suggests the gap could be even closer.
It found 51% of people are voting No, with 49% backing Yes, when undecided voters are excluded.
When those who are yet to make up their mind are factored in, the No campaign is on 49%, Yes on 47% and 5% said they do not know how they will cast their ballot.
The latest YouGov result remains unchanged from the last poll it conducted six days ago.
It excludes the “don’t knows”, who made up 6% of the survey.
It said its research also suggests men are more likely to vote for independence by a margin of 54% to 46%, while women would prefer Scotland to remain in the UK by a margin of 57% to 43%.
YouGov said the result was compiled after 3,237 electors were questioned between September 15 and 17.
The Panelbase survey came out less that 24 hours before voting gets under way in the referendum and was another indication that the campaign over the future of the UK could go down to the wire.
Exactly half (50%) of the 1,004 people who were questioned said they would be voting No to independence, with 45% voting Yes.
Just one in 20 (5%) of voters have still to make up their mind, according to the research.
It added men continue to be more likely to support Scotland leaving the UK, with 54% of all males who were questioned said to be Yes voters, ahead of 44% who are voting No and 3% who are undecided.
Just under two-fifths (39%) of women questioned said they would be voting Yes, with 54% backing No and 7% still undecided.
Survation also released its final poll on the referendum, which suggested 53% of voters will support Scotland remaining in the union while 47% will vote Yes - when undecided electors are excluded.
When the 9% of those unsure how they are voting are included, the No campaign received 48% while Yes picked up 43%.
The poll for the Daily Record was conducted by telephone over a 24-hour period on September 16 and 17.
Survation said the poll managed to reach 1,266 respondents but has an effective sample size of 1,089.
Blair Jenkins, Yes Scotland chief executive, said the opinion polls showed the Yes campaign is in “touching distance of success”.
He said: “The referendum is on a knife edge and this will spur on everybody who wants and is working hard for a Yes to redouble their efforts.
“People know that a Yes vote is Scotland’s one opportunity to achieve job-creating powers, protect our NHS from the damaging impact of Westminster cuts and privatisation and ensure that never again do we get Tory governments imposed on Scotland that we have roundly rejected.
“The empty offer of a very few more powers from the No campaign has unravelled within 24 hours, in the face of a Tory revolt at Westminster.
“Only a Yes vote can secure all the powers that Scotland needs to create more jobs and secure our NHS for the future.”
Mr Jenkins said the campaign was “working flat-out” to ensure a Yes vote, explaining this was because “it’s the biggest opportunity we will ever have to build a fairer society and more prosperous economy”.
He added: “This referendum is unlike any that has been held before because of an expected record turnout - which we believe will favour the Yes vote.”