The online survey conducted by Awaz FM showed 57% of listeners backed the idea of Scotland an independent country, while 37% said no.
However, the gap has narrowed since the radio station last conducted a poll on the subject, in February. At that time, the Yes vote was 64% while support for No was 32%.
With the narrowing in the polls, both sides of the campaign are actively engaging with Scotland's various ethnic communities, ranging from the established Asian and Chinese groups to more recent arrivals from Eastern Europe and Africa.
Last week the Muslim Womens' Association of Edinburgh held a debate in the city's Central Mosque. Human rights lawyer Aamer Anwar represented Yes. Recently an Africans for an Independent Scotland group was launched, as well as a Nigerians for Yes.
According to anecdotal evidence, some Asians have told activists they are favouring independence in order to "get one back on Britain", for its colonial rule of India and subsequent partition of the country in 1947.
But speaking to a Middle Eastern TV network at a community event in Glasgow, Labour's Anas Sarwar said the vote was not a referendum on Britain's past. He said: "When I go back to Pakistan to visit my father, who is now the Governor of the Punjab, at his official residence, there are portraits of 50 other Scots who have held the same position. It would be wrong to suggest that Scotland or Scots were bystanders during the British Empire."
Another Labour source who was campaigning in Pollokshields said many first-generation Asian business owners told him: "We came to the United Kingdom in the 1960s and 1970s and now 40, 50 years later we want to remain as part of the United Kingdom."
The General Secretary of the Scottish Asians For Independence (SAFI) said his organisation aimed to increase its activity as the date of the referendum gets closer.
Tahir Mohammed said: "SAFI has worked hard in the Asian communities who have historically voted Labour … the likes of the late Bashir Ahmed MSP and Humza Yousaf MSP have given us an alternative."