Stead said a decision on the 34-year-old’s condition will be made after the seamer consults with specialists back home.
Until then, we can’t draw conclusions about the World Cup. We just need to understand the timeline and what it looks like and once we have that information we can move on and make a decision. We want to give Tim every chance to prove his fitness. There will be an element of uncertainty as it is a broken bone and at some stage he will have to start catching balls and bowling again.
The healing process in the next 10-12 days will be very important for him as well, Stead told reporters.
The Black Caps, who lost 1-3 in the ODI against England, travel to Bangladesh for the three-match ODI series starting on Thursday.
Before opening the tournament, they will play Pakistan and South Africa again in World Cup warm-up matches on September 29 and October 2 respectively.England on October 5.
Southee, who last played in India in 2011, will be playing in his fourth ODI World Cup.
Teams can make changes to the 15-player World Cup squad until September 28, after which any changes must be approved by the ICC.
New Zealand lost to England by a boundary score in the 2019 World Cup final at Lord’s after the teams failed to share a draw at the super-over.