The YouGov poll for The Times suggests that in the final round of voting, Mr Corbyn would get 53% of support, six points ahead of Andy Burnham.
Shadow minister Tristram Hunt warned a Corbyn victory could reduce Labour to the status of a pressure group.
Yvette Cooper and Liz Kendall are the other candidates for the leadership.
The YouGov poll suggests Mr Corbyn is the first preference for 43% of party supporters, ahead of Andy Burnham on 26%, Yvette Cooper on 20% and Liz Kendall on 11%.
Taking second preferences into account the poll, of 1,054 people eligible to vote in the contest and carried out between Friday and Tuesday, pointed to a 6% Corbyn victory.
Tony Blair is to make a rare speech to Labour activists as turmoil grows after a poll suggested left-winger Jeremy Corbyn was ahead in the leader contest.