Buchanan finished yesterday; Littlejohn will stay until September to see out his contract.
"The person has to have good knowledge of first class, and preferably, international cricket and have good local knowledge," White said of the selection manager role.
"It's very important they are well connected and respected and has good networks in New Zealand.
"We want the best person for the role, but if two people have equal ability we'd go for the New Zealander."
However, White did not believe the heavy Australian presence was necessarily a negative.
"I don't think the influence was over the top. They're good quality people," he said.
Of the two, Littlejohn, a former bowls administrator, is said to have been a solid structures man.
Buchanan, a former Australian coach, simply couldn't get on the same wavelength as former coach John Wright and incumbent Mike Hesson.
NZC yesterday said Buchanan, who was hired in early 2011 through to the 2015 World Cup, had opted to move back to Brisbane for family reasons. White confirmed Buchanan would be replaced, but the role might have "a small tweak" once it's advertised in two to three weeks.
"We are going to have someone head our high-performance department but we want to sit back for a couple of weeks and think about the role and maybe tweak it slightly."
The Herald understands Buchanan was, if not a dead man walking, at least on thin ice several months ago. The description "gardening leave" was mentioned at the time, and fiercely scotched by NZC. It is understood lawyers have been heavily involved in the Buchanan-NZC parting.
"It will be a high priority for our organisation to get a high-quality person in to do that job," White said, limiting himself on Buchanan to saying, "John did some good things for NZC".
NZC also revealed a rubber stamping of the selectorial arrangements for national teams yesterday.
The coach of the national men's and women's teams will be selectors along with the national selection manager, but the coach will have the final say.
The reverse will apply for New Zealand A and under 19 teams, wherein the selection manager's opinion will hold sway.
The argument is that having a more holistic perspective for those teams enhances the view of the selection manager, whereas the coach's perspective would necessarily be narrower.
"All we're doing is providing clarity. This is the norm is most sports. Ultimately the head coach is accountable for performance and this structure reinforces that," White said.
