The 24-year-old injured his elbow in the Indian Premier League (IPL) 2016 while playing for Royal Challengers Bangalore and was subsequently ruled out of the tournament.
"Milne is just coming back from a wee tidy-up elbow operation he had. He's travelling nicely and he's going to play in those games, but we are keen to keep expanding his batting game so he's going to play as a batsman," national selector Gavin Larsen was quoted as saying by stuff.co.nz on Wednesday.
"It's probably fair to say that it would be a stretch (for him to make the squad for India)."
Among other bowlers, all-rounder Corey Anderson, who is recovering from a back injury, however, reportedly has a brighter chance of making the squad for the ODIs in India.
He will be part of the Emerging Players XI team in the three one-dayers against New Zealand XI.
"We will monitor Corey, like we'll watch everyone, and assess where he is at after those games. It is the bowling obviously we are very keen to see Corey keep progressing in, to be getting back to being selectable as a genuine allrounder. We are trying to get that on track as quick as possible," Larsen said.
