The British Election Study (BES) analysed data on voting intentions collected in March and June, which showed that those who said they did not know how they would vote in March were more likely to back Yes three months later.
March's survey showed 52% support for No compared with 37% for Yes, with the rest undecided.
There was little change in these headlines figures in June, with 51% backing for No, 39% backing for Yes and 10% saying they did not know.
Of those who said "don't know" in March, 25% said they would vote Yes in June, 18% said they would vote No while the remainder still did not know.
"If all the remaining 'don't knows' moved from undecided to Yes in exactly the same proportion as those between March and June, the final result would likely be Yes 44% and No 56%," researchers said.
They also found that the economy is one of the most important factors which would persuade voters to change their vote to Yes.
Professor Ed Fieldhouse, from the University of Manchester, co-director of the study, said: "The BES is unique in that it is able to track the referendum vote intention of the same voters over time.
"The data tells us that the vast majority of those intending to vote Yes or No did not change their mind in the three months between March and June.
"However, the don't knows are still significant. We find they are more likely to vote Yes when the time comes.
"But our data also shows not enough of them will support the Yes camp to win the eventual race: more people are yet to be persuaded."