Latest figures from the Northern Ireland Life and Times Survey suggest there is still a substantial majority in favour of Northern Ireland remaining in the UK.
The survey, which was set up by Queen's and Ulster Universities, found that 55% of those interviewed would vote for Northern Ireland to remain in the UK.
This compares to only 22% who said they would back a United Ireland.
Last week, the BBC published a survey that suggested a much tighter race.
Responding to the Northern Ireland Life and Times Survey, 12% said they would not vote and the remaining 10% said they did not know how they would vote.
Different numbers
According to the BBC's survey on identity, which was carried out by the Belfast pollsters Lucid Talk, only 47% of people in Northern Ireland identified themselves as strongly British.
The online and telephone survey said that 45% of respondents backed staying in the UK and 42% favoured a United Ireland. This left undecided voters potentially playing a crucial role.
Last month, an Ipsos Mori poll conducted face to face indicated that 50% favoured staying in the UK, whilst only 21% backed a United Ireland.
Some 33% of those interviewed for the Life and Times Survey said that they think Brexit has made a United Ireland more likely, whilst 9% believe it has made it less likely and 43% believe it makes no difference.
Asked whether Northern Ireland will be financially better off when the UK leaves the EU, 41% disagreed and 18% agreed.