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But the man behind the move, Dunedin city councillor Jim O'Malley, is keeping his cards close to his chest - at least for now.
Cr O'Malley has put forward a notice of motion, to be debated at next week's full Dunedin City Council meeting, seeking a change to Local Government New Zealand rules.
The change, if supported by councillors and approved by LGNZ, sought to change eligibility rules for the role of LGNZ president.
At present, the role could be held by a current elected member, although it was typically filled by a council mayor or chairman.
Cr O'Malley's idea would widen that eligibility, by allowing any mayor or chairman who had held an elected post within the last five years to act as LGNZ president.
Cr O'Malley would not discuss his idea yesterday, saying he did not want to ''pre-empt the discussion'' at next week's council meeting.
''So I will wait until all councillors have had a chance to comment on the motion at Tuesday's meeting before making a statement.''
Mr Cull, contacted in China, would only say he did not support Cr O'Malley's move, ''but [I] think it appropriate to leave discussion of it until the council meeting''.
Mr Cull planned to be back in Dunedin in time for next week's meeting.
The Otago Daily Times reported yesterday Mr Cull was still ''seriously undecided'' about whether to stand again for mayor, amid rumours he might be preparing to step aside.
He expected to make a decision ''in the next month, I would imagine'', and whether he wanted to try to continue in his LGNZ role was among the factors being considered.