A poll by TVNZ's Q+A programme this morning had Mr Cunliffe as the early favourite.
The telephone poll of 517 people showed he had 29 per cent support from voters across the political spectrum followed by Jacinda Ardern on 15 per cent, Shane Jones at 11 per cent, Mr Robertson on 10 per cent, and Andrew Little on 9 per cent.
Both Ms Ardern and Mr Little have ruled themselves out of the leadership race, while Mr Jones is yet to declare either way.
Mr Robertson this afternoon said he wasn't concerned by those numbers.
"It's early days and this is one of those occasions when you can say there's only one poll that matters, it's a poll of MPs members of the party and affiliated unions and that's the poll I'm focused on."
The leadership contest will be decided over the next three weeks. Voting will take place by post and at a series of meetings beginning next Saturday with the final result expected on September 15.
Mr Robertson did not expect the fact he is gay would affect his chances during the selection process or at during next year's election campaign if he is selected.
"I think New Zealanders are more concerned about whether they've got a job, can they put food on the table, have their kids got a good school to go to than they are about my private life."