A YouGov poll for The Times newspaper said support for a "Yes" vote has fallen to 35 per cent, while 54 per cent would vote against independence, and 12 per cent were undecided or would not vote.
With undecided and non-voters stripped out of the survey, which was carried out at the end of June, the result of 39 per cent "Yes" is down three per cent from the comparable figure in March.
Support for independence initially rose after Salmond announced his referendum plan in 2010, but has plateaued in recent months and now seems to be falling.
Speaking to AFP on Saturday, Salmond was bullish.
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"We're closing all the time... We've got a bit to go but we're travelling in the right direction," he said.
The economy has been a major battleground, with independence activists saying a split would benefit Scotland but unionists warning of harm to both countries.
The British government has warned that Scotland would be forced to ditch the pound sterling in case of independence, and that an independent Scotland may be forced to reapply for European Union and NATO membership.
Salmond says North Sea oil revenues would boost Scotland's economy.