He has made the number four slot his own since 2019, scoring both his ODI hundreds at that position, but Shan Masood and Abdullah Shafique have been given the place in the opening two games of the five-match series.
While Rizwan has excelled in the finisher's role at five, helping his team win both games, he said he did not want to stay there.
"If you ask me honestly, I am not happy batting at number five (in ODIs), because I want to bat at number four," he told a news conference on Monday.
"But it is not important that I get what I want.
"The captain and coach will do what they like. It is my own wish to bat at number four. But I have not complained to anyone."
Rawalpindi hosted the first two ODIs but the series now switches to Karachi for the remaining three. The teams are scheduled to resume the series with game three on Wednesday.
New Zealand are without injured captain Kane Williamson and several frontline players taking part in the Indian Premier League.
The tourists also trailed the preceding Twenty20 series 2-0 before fighting back for a 2-2 draw and Rizwan said Pakistan must not get complacent.
"We want to forget the past, the good and the bad," Rizwan said.
"The conditions and requirements in Rawalpindi were different.
"We will assess and adapt and look to win the series. That will be our focus."
