New Zealand have to name their World Cup squad of 15 by September 5, a month before the tournament begins with them playing England on October 5 in Ahmedabad. Any number of changes to the squad, however, can be made until the last week of September after which further changes will require ICC approval.

"Kane's working very much on a day-by-day, week-by-week process and we've been really clear and careful with him that we don't look too far ahead and, I guess, get expectations too big or not big enough at times as well. He's progressed as we've hoped and possibly even better in some cases but you know with ACL injuries that they can be difficult, and different for every person as well. As I said, we'll try and get the medical experts around Kane as much as we can to help us make that decision in about three weeks' time."

Tom Latham will lead New Zealand in England in Williamson's absence, and will continue as captain in the World Cup as well if Williamson doesn't make it. When asked if Williamson would be selected for the latter stages of the tournament if he recovers in time for the knockouts, Stead said it was under consideration but unlikely.

"That's something we are talking about at the moment," Stead said. "If it's the knockout stages then I think that might be too late because you're saying something that may or may not even be there. But if it was earlier in the World Cup, I think we'd definitely be considering it.

"He's not facing bowlers as yet but he's basically doing everything else. Obviously, with the knee and the way it is, we're just being careful on how that twists so he's still in that healing and rehab phase. It's getting that fine balance of pushing him as far as he can go but making sure we don't cross that line and do more damage. He's been extremely diligent, we couldn't have asked more from him in that space and it's encouraging to see where he is at and how he's going. That doesn't promise that he's going to be part of the World Cup squad just yet, that's just something that time will tell."

After Williamson returned to train in the nets in Tauranga, New Zealand took the decision to fly him to England to reintegrate him into the squad and also draw from his experience of having played the previous three ODI World Cups. New Zealand have only two ODI series remaining before the event, one in England and the other in Bangladesh in September.

"In terms of him being there (England), he'll be getting a bit of training under his belt, being in and around the squad," Stead said. "Kane's been to a number of World Cups and he's been a key player for us for a long, long time. Leaning on his experience as well will be important to the group but alternately it's about seeing is he going to be ready or not for us and that's something only time will tell.

"Couple of weeks ago we were in Tauranga to see him with the bat back in the hand. Injuries like this can often prolong people's career as well and I think as long as we're talking about Kane Williamson playing for New Zealand for a long period of time, that's exciting for New Zealand cricket."