"We're hopeful he'll be right for the T20 [against Zimbabwe on Sunday] and South Africa beyond that."
New Zealand used 12 of their 15 players in the first two ODIs, which were split 1-1, with Milne, fellow seamer Ben Wheeler and batsman George Worker - who's on his first tour - not required yet.
The only change for the second game, won on the back of Martin Guptill and Tom Latham's unbroken 236-run opening partnership, was Colin Munro in for Jimmy Neesham.
Thanks to Guptill and Latham's fine display, Munro didn't get a chance with the bat. It would have been frustrating on a personal level for the Aucklander, who will be thirsting for a chance to push his credentials.
Still, New Zealand must feel they have Zimbabwe's measure after an unsatisfactory display in the opening seven-wicket defeat.
With South Africa having named a strong squad for New Zealand's visit, it's important the tourists arrive in the republic in winning form.
AB de Villiers is back to lead South Africa in the three-game ODI series. His squad is full of familiar heavyweight names, apart from tall seamer Morne Morkel and lefthand batsman JP Duminy who each have leave for the birth of their first children.
The most unusual name in the squad is Morne van Wyk, who was behind a microphone during their recent series against Bangladesh. He replaces the out-of-sorts Quinton de Kock and is expected to keep in the ODI series.
Van Wyk, 36, has had a sporadic career of 14 ODIs over 12 years, but if he fancies this as an Indian summer in his career, the words of coach Russell Domingo will have put him right on that: "It probably is a short-term solution until someone else steps up ... to do the job."
