Mr Jones has ruled out running for leader, saying he did not have the numbers, but has not ruled out a shot at deputy. If he does stand, it is unlikely to be on any one ticket so he could work under any leader, although he is likely to prefer Mr Shearer or Mr Parker.
Some in caucus believe he would add critical firepower to a new front bench against Winston Peters and National as it undertook asset sales.
Yesterday, Mr Jones did not want to comment on the leadership options, but said Labour should not treat its bad result as "a minor aberration".
"Really, we've got to delve deeply into why three out of every four New Zealanders who cast a vote said we were unsound and unfit to govern."
Mr Cunliffe and Mr Parker are so far the front runners in the contest and both said they were not taking anything for granted before the secret ballot on December 13. But Mr Shearer's last-minute inclusion surprised some and could alter the race if it takes support from Mr Parker.
Although some Labour members outside the party were lobbying for Mr Shearer, he was not expected to put his name in.
Yesterday he said he would talk to his colleagues and see if there was any support before he formally entered.
"At the moment I'm just making some soundings."
It is also still possible that Mr Robertson could stand as leader, rather than as deputy to Mr Parker.
Mr Cunliffe acknowledged the work of Mr Goff and Ms King, but said Labour needed to change if it was to regain government. He said he was honoured Ms Mahuta had agreed to be his running mate.
There are also concerns the two-week campaign will turn nasty and split the party. Mr Cunliffe is already trying to fend off claims about his campaign performance, including that he failed to ensure Mr Goff was prepared for a debate against Mr Key and took days off at a critical stage. Mr Cunliffe said it was "nonsense".
All contenders and other MPs spoken to welcomed the open contest.
Mr Goff yesterday refused to say which of the contenders he would support, although it is understood he favours David Parker.
He pledged his "full and active support" to whichever team won the contest and looked forward to working 60-hour rather than 100-hour weeks.
THE THREE DAVIDS
David Cunliffe:
"Our aim is to win 2014 back for New Zealand and for a rejuvenated Labour Party ... there will be reorganisation, there will be some new management systems, there will be rebranding and I think you'd see a very rejuvenated face of the Labour lineup by the new year."
David Parker:
"In the past, Labour fought and won victories for the working class. To be relevant today, Labour has to change to be the party of today's working people. Yes, we must look after the vulnerable, but we have to be more than that and reconnect with working people."
David Shearer:
"I think I can contribute to the Labour Party. I think we need to go back and refresh the Labour Party. It needs to have a new look and be able to carry the aspirations of New Zealanders."