Labour Napier MP Stuart Nash said he "might" consider the position of deputy leader if it was presented to him by party hierarchy.
"It is up to the leaders to determine who they want," he said.
Mr Nash was touted as a possible leader of the party after its poor showing in the general election but said he was not interested.
David Cunliffe resigned as leader following the party's poor performance in the general election but said he still wanted the job.
So far Grant Robertson is the only other contender.
Mr Nash said it would be interesting to see if any others put themselves forward.
"I wouldn't make any decision until after that leadership battle has been decided.
"At this stage it certainly hasn't been discussed and I'm not expecting it."
Mr Robertson was Labour's deputy leader in 2011 under leader David Shearer and contested the leadership in 2013 leadership, won by Mr Cunliffe with David Parker as deputy.
Like Mr Nash, Mr Robertson has not held a ministerial role.
Meanwhile, Labour's New Zealand Council has released the terms of a comprehensive review of the party, including its organisation, campaigning, political positioning and relationship with other parties, after its dismal result in last weekend's election in which it got 24.69 per cent of the party vote.
Most of the review will be finished by December, which means it will be done parallel to the leadership contest triggered by Mr Cunliffe's resignation, and to take effect after caucus on Tuesday. President Moira Coatsworth said the names of the reviewers would be named in the next week.