New Zealand Cricket confirmed the team's top batter will be part of the squad for the 50-overs tournament in India starting in October, some six months after he ruptured an anterior cruciate ligament in the Indian Premier League in early April.

Back near 100% in terms of his batting movement in the nets at training, Williamson said the next three weeks would decide whether he would be fit for New Zealand's opener against England, a rematch of the 2019 World Cup final.

"That would be great but all the way along it truly has been just managing things day-to-day, following the programme as closely as I can and hoping that could be a possibility," he told reporters on Tuesday.

"I'll certainly know more in the next three weeks."

Williamson said he was still some way off being able to run at full tilt but was making good progress.

"Currently I'm getting through those sessions reasonably well. Then it's a little bit more change of direction," he said.

"There's still some time left to keep taking some steps forward."

Williamson will likely have no choice but to go into the tournament without any match practice but shrugged off the challenge.

The knee injury follows an elbow problem that dogged the New Zealand skipper for more than a year and continues to be managed.

"The elbow's feeling good, thank you for asking," Williamson said with a wry smile.

"Working through injuries is a little bit of a part of the job. So trying to do it well and be ready for whatever's next and possible is the goal."