Labour Party officials in Te Atatu are understood to have thrown their weight behind their MP, Chris Carter.
Mr Carter was suspended from the Labour Party caucus for circulating an anonymous letter detailing discontent with Mr Goff and predicting a leadership challenge.
A special meeting of his Labour Electorate Committee was held on Saturday.
While members of the committee are not talking publicly, one said Te Atatu had produced three cabinet ministers and Chris Carter was the only one to remain loyal to the party's grassroots.
It is understood the results of a vote supporting Mr Carter will be sent to Labour Party president Andrew Little next week.
Mr Little said on Saturday he had not been told of the outcome of the vote.
He said the central governing body, the Labour Party Council, will consider the results of the vote when it meets next weekend.
Harre won't contest seat
The former Alliance cabinet minister, Laila Harre, says she will not put her name forward as a Labour Party candidate for the Te Atatu electorate.
Ms Harre had said that standing for the seat was something she would consider in the right circumstances.
But on Sunday she told Radio New Zealand News she had changed her mind, and wants to go ahead with her two-year posting in Fiji for the International Labour Organisation, with no distractions.
