Mr Robertson would not confirm last night that he had shifted his support to Mr Shearer but said he held Mr Parker "in the highest regard personally and as a politician".
Mr Cunliffe's running mate is Hauraki-Waikato MP Nanaia Mahuta.
The choice for Labour MPs will be stark.
On the one hand, there is the popular but inexperienced Mr Shearer, a protege of Labour leader Phil Goff.
On the other, the less popular Mr Cunliffe - an MP for twelve years, a former diplomat and a protege of former Prime Minister Helen Clark.
Mr Robertson, the Wellington Central MP, was originally paired with Mr Parker when Mr Goff said on Tuesday that he would resign.
But it became evident even then that Mr Robertson harboured notions of putting himself forward. Others have counselled him against it.
It is not clear yet whether Mr Shearer will pick a running mate. If he does, it is possible that Mr Parker could be his choice.
It is also possible that Mr Robertson could become Mr Shearer's running mate. Together they would represent a complete break from Labour's past, both having been in Parliament for only one term and neither having served in a Cabinet.
And Shane Jones is also an outside chance as a running mate. He and Mr Shearer together would represent a return to a more pragmatic party, with less emphasis on gays and feminists.
One of the MPs helping Mr Shearer is Damien O'Connor (West Coast-Tasman), who said last term that the party was dominated by "a gaggle of gays and self-serving unionists".
Mr Parker's withdrawal came only hours after party president Moira Coatsworth set out a schedule for the contenders to present themselves to party members at meetings in Hamilton on Monday, Palmerston North on Tuesday, Wellington on Wednesday, Christchurch on Thursday, Dunedin on Friday and Auckland on the following Sunday.