Justice Minister Amy Adams has ruled herself out of the contest for National Party leader, and Prime Minister.
However, she was leaving the door open for the position of deputy.
Health Minister Jonathan Coleman, one of the three leadership contenders, named Ms Adams as one deputy he could work with.
MPs will choose from Dr Coleman, Deputy Prime Minister Bill English and Police Minister Judith Collins - and anyone else who might put their hat in the ring - in a special caucus meeting on Monday.
Ms Adams said she would not be on that ballot.
"It's still very early in the process but I'm not intending to stand for leader."
She said she had not made any decision about whether or not to run as deputy.
"But I certainly haven't made any commitment to any of the people who are standing, and any suggestions of me being on any ticket are purely speculation."