Those interested in the selection for National include business director Rachel Afeaki–Taumoepeau, health professional Dr Frances Hughes and former Mayor Andrew King.
The party's board vets those nominated, and a selection panel then decides on a shortlist of a maximum of five. Members of the local electorate then make the final decision on who will stand as National's candidate.
Candidate nominations close today ahead of the byelection on December 10.
Luxon has repeatedly referenced his commitment to improving diversity within the party, particularly after the mockery over the photos of the four Pākehā men in blue suits who comprised National's shortlist to contest the Tauranga byelection earlier this year.
"We've [got] a lot of work to do in the National Party and that's why we've gone through candidate selection and our processes to make sure we're getting rid of unconscious bias, we're opening up to new talent pools," Luxon said this week.
Luxon recognised the final decision on candidacy sat with local party members, but said he had "set expectations" on the profiles he wanted added to the caucus.
While he couldn't guarantee National's pick for the Hamilton West byelection would represent the priority placed on diversity, Luxon was confident it would be shown in the party's candidates for next year's general election.
Labour, meanwhile, seems to have lower interest to run in the byelection forced by the resignation of Gaurav Sharma after his expulsion from the Labour Party last week.