Many expect the contest to come down to Mr Little and Mr Robertson, but Mr Parker appears to have more caucus support than Mr Little.
Mr Little, however, is expected to attract the majority of the affiliated unions' votes, and Ms Mahuta seems likely to be the first one eliminated in the preferential voting system.
That means second and possibly third preferences will be crucial. Candidates are said to be lobbying as strongly for second preferences as for first.
If no candidate wins more than 50 per cent of the vote on first preferences, the bottom candidate drops off and his or her preferences are distributed.
Caucus votes will account for 40 per cent of the vote; ordinary membership 40 per cent; and 20 per cent from seven affiliated unions, allocated according to size.
On current soundings, Mr Parker's support is weighted to male MPs and Ms Mahuta's to Maori and Pacific MPs.
Mr Robertson has retained all of his support from the contest after David Shearer's resignation last year when he and Shane Jones lost to David Cunliffe.
Voting has started and the result will be announced on November 18.
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Caucus numbers
Andrew Little 6: Andrew Little, David Cunliffe, Iain Lees Galloway, Sue Moroney, Carmel Sepuloni, Poto Williams
Nanaia Mahuta 6: Nanaia Mahuta, Peeni Henare, Adrian Rurawhe, Su'a William Sio, Louisa Wall, Meka Whaitiri
David Parker 9: David Parker, Clayton Cosgrove, Kelvin Davis, Stuart Nash, Damien O'Connor, Jenny Salesa, David Shearer, Rino Tirakatene, Phil Twyford
Grant Robertson 11: Grant Robertson, Jacinda Ardern, David Clark, Clare Curran, Ruth Dyson, Kris Faafoi, Phil Goff, Chris Hipkins, Annette King, Trevor Mallard, Megan Woods
An estimate of where the numbers sit at present in the caucus.
