The poll published in To Ethnos newspaper showed the "Yes" campaign slightly in the lead but well within the margin of error. It also showed an overwhelming majority -- 74 per cent -- want the country to remain in Europe's joint currency, the euro, compared to 15 per cent who want a national currency.
Prime Minister Alexis Tsipras called the referendum last weekend, asking Greeks to decide whether they should accept creditor reform proposals in return for vitally needed bailout funds. He is advocating a "No" vote on Sunday.
The "Yes" campaign says the referendum is in fact a vote on whether Greece wants to remain in the euro and in Europe.
The government rejects this as scaremongering, saying a "No" vote will put it in a better bargaining position and will not lead Greece to leave the eurozone.
Also Read
The survey conducted by ALCO found 41.5 per cent will vote "Yes" on Sunday and 40.2 percent saying they will vote "No," with 10.9 percent undecided. The rest said they would abstain or leave their ballots blank.
The survey interviewed 1,000 people nationwide on June 30-July 1 and has a margin of error of 3.1 per cent.
The referendum campaign will wrap up this evening with rallies by the two sides, to be held 800 metres apart in central Athens.
Tsipras is set to speak at the "No" rally in the capital's main Syntagma Square outside Parliament, while the "Yes" rally will be held at the nearby Panathenian Stadium, where the first modern Olympics were held in 1894.
The government vehemently denies a "No" vote would force the country out of the euro, but most opposition parties and many European officials have said this could be the case.