"Lockie has a little ab injury at the moment. We're just managing just that and the most important thing is we get to the start of the World Cup and Lockie is ready to go," Stead said. "He's a very, very important cog in our bowling line-up. Unfortunately for him, he missed last year's World Cup with the injury he had then. I mean we are mindful of it and we want to make sure that he's right and ready for those early games in the World Cup.
"There is that chance [of him missing the entire tri-series]. We will just see how he responds to treatment over the next few days."
On Saturday, New Zealand picked Blair Tickner ahead of Milne.
"It's the first time I've had eyes live on Milne at the nets and he looked really good," Stead said. "We're pleased with what we are seeing there and again he is coming off a reasonably extensive injury break as well, so just managing him and making sure he's right will be the most important thing for us in these four games."
Mitchell hopes to be fit for T20 World Cup
Mitchell, who was hit on the little finger of his right hand while batting in the nets on Friday, is hopeful of recovering in time for New Zealand's World Cup opener against Australia at the SCG on October 22.
"Obviously, not ideal timing but we've got some good news around where the fracture is in the hand and the time frame to be ready for the first game in Australia in a couple of weeks' time," Mitchell told Spark Sport on the sidelines of New Zealand's tri-series opener against Pakistan on Saturday. "We'll do everything we can to try and be ready and fingers crossed that I'll be good to go.