Around 1,000 people were asked by pollsters Ipsos-Mori if they would consider switching to Yes if they thought it would be the only way to keep a separate Scottish football team.
Some 3% said they would definitely switch to Yes, while 6% said they would at least consider it.
However, there would be little impact on the outcome of the referendum if every concerned Tartan Army fan defected, with support for the union holding its majority at 56% against 36% support for independence.
Ian Coldwell, managing director of Pagoda PR which commissioned the poll, said: "Analysis by polling expert John Curtice indicates that the way people feel inclined to vote on independence depends more on how British they feel rather than how Scottish.
"Nearly everyone in Scotland feels Scottish, but Scots differ in how British they feel. If levels of support for Yes and No move closer together, this kind of issue could have an impact."
The poll initially found that 31% intend to vote Yes to independence, with 59% voting No and 10% undecided.
Support for independence rises to 33% if concerned Tartan Army fans who would definitely switch to Yes are included, and to 36% if those who would consider a switch are included.
Support for the union falls to 58% if concerned Tartan Army fans who would definitely switch are deducted, and to 56% if those who would consider a switch are removed.