Mr Ellison, of Otakou, has expressed concern about having a new selection process, believing the party should have chosen the first runner-up from February's selection, following the sudden death of candidate Monte Ohia in June.
Mr Ellison and lawyer Rahui Katene were the two other nominees for the Maori seat, which is the largest electorate in the country, in February.
No runner-up was announced following the voting, which used the single transferable vote system.
Mr Ellison also asked if the party had a new candidate it wanted to field, but this was emphatically denied by Prof Winiata.
"Absolutely not. There is no-one preordained, no secret plan."
The party wished to have a process which was fair, with as much participation as possible within the given time constraints.
Prof Winiata said the party's national council could have chosen to select the runner-up, as Mr Ellison suggested, but decided against it.
The reason for this was that at the selection earlier this year, which involved a series of hui at which candidates spoke, there was not a big turnout of party members.
At the time, the council had considered whether there should be another round of hui before the selection was made.
It was decided, however, that since the support for Monte Ohia was clear from the voting, and he had also been supported as the candidate at the 2005 election, that there was no need to go back.
After Mr Ohia's death, the party was faced with finding a process consistent with its constitution and electoral law and which could be completed reasonably quickly, Prof Winiata said.
The Maori Party rules say candidate selection shall be based on the principles of transparency, fairness, participation, reasonable notice and inclusiveness.
Under the announced process for Te Tai Tonga, nominees have to be nominated by at least 25 financial members by Saturday, with candidates being publicly announced on Monday, July 7.
The process will involve hui throughout the electorate, which encompasses the whole of the South Island and Wellington.
Electorate party members will gather to discuss potential candidates and vote on them using STV.
It seemed likely there would be some opportunity for candidates to speak, but some may not be able to attend all meetings.
Voting has to be completed by July 13.
Prof Winiata, who asked Mr Ellison at the weekend to reconsider his decision against standing, said there was still a possibility Mr Ellison's supporters could express their wish to have him stand.
He said he was not aware of any other formal expressions of concern about the process, although he conceded some of Mr Ellison's supporters may share his views.
Mr Ellison said on Monday, although Prof Winiata had done much to "ease me through some of the issues" in their discussion, it had not altered his decision not to stand.
