Boult (upper leg) and Taylor (calf) were injured in the drawn first Test in Dunedin and missed the eight-wicket second Test defeat to the Proteas at the Basin Reserve, which ended inside three days on Saturday.
The 27-year-old Boult had said during the match that he had been close to being available for the game and McMillan added on Sunday that the left-armer had been bowling in the nets.
Like Boult, Taylor will join the squad in Hamilton but McMillan said it was still too early to know whether the experienced batsman would be available for a Test New Zealand must win to level the three-match series.
"You can't take players into a Test against South Africa who aren't fully fit," McMillan said.
"I haven't spoken to him for a couple of days but I'm sure he is keen. He loves playing there and he's done well in recent times."
Taylor's potential return would solidify a New Zealand batting lineup which was humbled by South Africa in the second Test.
South Africa's left-arm spinner Keshav Maharaj took a career-best 6-40 in the second innings despite the ball not turning appreciably on what was a good batting wicket.
Pundits criticised some of the selection decisions, particularly going in with only two frontline seamers and trying to bolster the batting with all-rounders Jimmy Neesham and Colin de Grandhomme.
The pair scored a combined total of 23 runs in Wellington and took only four wickets between them, even if de Grandhomme's 3-52 in the first innings had helped reduce South Africa to 94-6.
Opener Tom Latham is also woefully out of form, having scored 10, 8 and 6 in the two Tests against the Proteas after notching scores of 7, 0, 0, 2 and 0 in the five one-day matches he played against Australia and South Africa last month.
McMillan, however, said there were unlikely to be any changes to the squad for the final Test, which starts at Seddon Park on Saturday.
"We've got the best players in New Zealand in the squad," McMillan said. "They certainly showed in Dunedin that they are good enough to play well and compete.
"Yesterday they didn't stand up. Yesterday was a terrible day. To lose within three days is unacceptable and the group is hurting and disappointed."
First Published: March 19, 2017, 11:38 AM IST