In an interview on TVNZ this morning, Robertson refused to answer questions on whether he would like to be Labour leader.
"I'm not giving thought to that at this stage," he said.
He said it was for Goff to decide whether he wanted to remain as leader after the party caucus meeting on Tuesday.
Pundits including former National Party president Michelle Boag and Unite Union leader Matt McCarten touted David Shearer as a potential Labour leader on Q+A this morning.
Shearer defended his Mt Albert seat with a resounding majority and is tipped as a rising star within the party caucus.
He last night deflected any questions about the future Labour leadership.
As Cunliffe waited for Goff to arrive to give his concession speech last night, he refused to say if his leader would have his support today.
"I think Phil is a very good guy and he's a really valued caucus colleague but I'm not going into any broader issues tonight."
Asked if he expected Goff to resign he said he did not know what was in his leader's mind.
"That's a matter for Phil and no doubt there will be some thinking he will do but I'm not going there tonight."
Only one of the predicted Labour leadership candidates has already been ruled out.
Losing Tamaki-Makaurau candidate Shane Jones this morning told TV3's The Nation it was "highly unlikely" he would put his name in the hat for his party's leadership.
Jones refused to indicate who he would support in a leadership battle.