Cunliffe has previously said he wanted to stay on as leader if Labour did not win next weekend. "I think you can tell that I enjoy the job and I think we've done a fair fist of it, but beyond that I'm not commenting," he said yesterday.
"All my energies and all my focus is on winning this election. I believe we can win, I believe we will win, and I'm not going to be giving any thought to after the election until after election night."
When asked if Labour lost and Cunliffe decided he did not want to be leader again, 64.1 per cent said they either did not know who would be the best person, or refused to answer the question.
University of Otago politics lecturer Dr Bryce Edwards said Cunliffe would struggle to stay if Labour's vote fell below 25 per cent.
"If he does go there's no doubt in my mind that [his successor] would be Grant Robertson. There continues to be speculation about David Shearer or Phil Goff having a go but I don't see that as credible. David Parker has zero chance."
The poll showed former leader Shearer and Robertson were the most preferred if a replacement for Cunliffe was required, each receiving 7.8 per cent support.
Labour's deputy leader Parker received 5.6 per cent of support, followed by Jacinda Ardern at 5.1 and then Andrew Little at 2.3.
Former party president Mike Williams said he "wouldn't hazard a guess as to who might put their hand up", adding some potential contenders might be out of a job if Labour fared badly on Saturday.
Right-wing political commentator and lobbyist Matthew Hooten said at least three potential future leaders - Parker, Ardern and Little - were at risk of losing their list seats if Labour received less than 24 per cent of the party vote. "That really only leaves Grant Robertson and David Shearer ... I think Robertson would be the winner."
Massey University political marketing specialist Professor Claire Robinson also believed Robertson was "the next cab off the rank".