The poll commissioned by ÖSTERREICH newspaper carried out by the research company Gallup predicts the Freedom Party candidate Norbert Hofer would receive 51 % of the votes, with the independent Green-backed Alexander der Bellen receiving 49%.
Van der Bellen initially won the run-off presidential election vote in May - with just 0.6% of the vote - but will now have to go head to head again with Hofer after the Freedom Party challenged the election result.
The Constitutional Court ruled in July that irregularities with the way postal votes were counted - and by whom - meant that the election would have to be repeated.
The Gallup poll predicts a turnout in the election repeat on October 2nd of around 84%. Turnout in the first run-off election was around 72.7%.
It also suggests that 68 % of those asked will definitely vote for the same person again and 11% “probably” will.
Freedom Party supporters were found by the poll to be the least secure voters, with only 73% of FPÖ sympathisers sure they would vote for the same candidate.
That compares to 85% for Green party supporters and 79% for supporters of the Social Democratic party (SPÖ), which both supported Van der Bellen in the run-off.
A large majority - 56% - of those surveyed said they thought the election challenge and decision to repeat it damaged Austria's international image.