His remarks came as Labour MPs began arriving for their first caucus meeting since the election, with most saying they expect robust discussions.
The Labour caucus will have to choose between a ticket of Cunliffe and Nanaia Mahuta, or Parker and Robertson as their new leadership team - and although Mr Parker appears to have the edge, it is a close contest.
Leader Phil Goff is expected to tell his caucus he will stand down before Christmas and attention has begun to focus on his replacement.
Mr Parker said he was not denying he would put his name forward. However he would wait till after the meeting to comment further.
Mr Cunliffe said he had been sounding out his colleagues and the response was "encouraging."
He said the party needed to reconnect with its base after getting its lowest election result since the 1920s but would not comment on whether he believed he was the person to do that until after Goff's announcement.
"I want to honour Phil Goff and the role he's played. He's been energetic and true to Labour's values."
He expected the process around the leadership to be "robust."
Asked about a whispering campaign against him, including claims he had not supported Goff well, he said he believed the public would see through it.
"I'm not going to respond in kind. That's clearly people positioning for whatever comes after today. It's nonsense and you can take it with a big grain of salt."
Mr Cunliffe's move to sign up Ms Mahuta is a canny move that may test others in Labour's Maori caucus, such as Shane Jones and Parekura Horomia, who were expected to support Mr Parker.
As a Maori woman who represented a largely rural electorate, she would act as a counterbalance to Mr Cunliffe.
Mr Parker will run on a ticket with second term MP and campaign spokesman Robertson. The team is understood to have the backing of the current leadership team, although Mr Goff and Annette King are unlikely to openly endorse it.
Some are understood to be arguing Mr Robertson should stand as the leader on that ticket as a "fresh face" with Mr Parker as his deputy. However, he is relatively inexperienced and there are concerns about whether the middle-class New Zealand that Labour needs to win the support of was ready to accept an openly gay MP in such a position.
Mr Cunliffe's main supporters include Lianne Dalziel, and Charles Chauvel and Moana Mackey. It is understood he has offered them the whips' jobs if he wins the contest. Others likely to side with Mr Cunliffe include Ruth Dyson, Sue Moroney and most Auckland MPs, including Rajen Prasad, Darien Fenton, Louisa Wall and Phil Twyford. However his numbers have been weakened by the MPs who did not return to Parliament.
As well as Mr Goff and Ms King, those likely to support Mr Parker and Mr Robertson include Jacinda Ardern, Trevor Mallard, Clayton Cosgrove, Maryan Street, Kris Fa'afoi, Shane Jones, Damien O'Connor, Andrew Little and Chris Hipkins.
Many in caucus are undecided and some MPs said more time was needed to digest the election results and figure out who was best to take the party on.
If there is a widespread call for a slower process at the caucus meeting tomorrow, Mr Goff could be asked to stay on as leader until early February. He is unlikely to agree to stay longer.
The contest has already caused some antagonism. Mr Cunliffe supporters are angered by claims Mr Cunliffe did not support Mr Goff properly during the election campaign. Some have blamed him for not ensuring Mr Goff could use the party's costings in time for a critical debate against John Key.
Mr Jones has ruled himself out of contesting the leadership, and others such as David Shearer and Mr Little are too inexperienced.
If the new team struggles to make an impact for Labour in the polls its caucus is unlikely to wait a full term to replace them, as it did with Mr Goff. If that happens, others such as Mr Jones, Mr Shearer and Mr Little could step up, or Mr Robertson could take over.
THE CHIEF CONTENDERS
They have the same first name, both entered Parliament in 2002 and have a background in business. But they have very different styles.
David Cunliffe: New Lynn MP since 2002. Former diplomat and Harvard scholar, worked as business economist at Boston Consulting Group before entering Parliament with health and communications and information technology portfolios. Labour's finance spokesman since 2008.
* Pros: High profile, strong Auckland support base. Strong, sometimes evangelical speaker, intelligent. Gets attention.
*Cons: Vainglorious tendencies may turn voters off, especially against the self-deprecating style of John Key. Could polarise the caucus, but could be countered with the right deputy.
David Parker: Won Otago electorate in 2002, list MP since 2005. Former lawyer and businessman. Was Attorney-General until 2006 and then Minister of Energy and Climate Change in previous Labour Government. Labour's shadow Attorney-General, and economic development and associate finance spokesman.
*Pros: Intelligent, good on detailed policy. Has attempted to put his bookish image away and come across as a stronger personality. Generally well regarded, not a polarising figure.
*Cons: Lacks the presence of Cunliffe and has a bland public persona. Can get flustered under pressure.
