The survey also indicates that voters supporting three of the parliamentary parties do not share their position for or against the euro.
47 percent of Swedes backed a move to the euro with 44 percent against in the survey by Novus on commission from the Liberal party and published in Dagens Nyheter on Monday.
Male voters are more in favour of changing the Swedish kronor for the European single currency with 50 percent in favour and 42 percent against. Among women voters the corresponding figures are 44-46 percent.
There is however a majority in favour of joining the euro across the age groups, although the strongest opposition is among young voters under 30-years-old.
Novus interviewed 1,000 Swedes between May 5th and May 12th and asked how they would vote if a referendum were to be held today.
The last time Sweden held a referendum on the issue, in 2003, those against claimed 56 percent of the vote while 42 percent were in favour of adopting the euro.
The Centre party was the only Alliance party against joining the euro in 2003 and their position remains the same. Their supporters have however become more positive, according to the poll, with a majority in favour.
The Christian Democrat party position is in favour of the euro but there remains a strong opposition among their supporters. The same is the case for the Social Democrats.