Williamson ruptured the anterior cruciate ligament in his right knee while fielding for Gujarat Titans in the Indian Premier League earlier this month and the injury was expected to keep the veteran right-hander on the sidelines for the 50-over showcase that is scheduled to be held later this year.
But Stead said Williamson's recent surgery had gone well and he wants to give the 32-year-old every chance to recover in time to feature in another New Zealand World Cup campaign.
"Look, it's still far too early to know," Stead said of Williamson.
"He's had the operation and, to date, what we know, that's been successful. So he is in the very, very early stages of his rehab programme.
"It's obviously pretty non-weight-bearing at this stage, and he's in a brace. So, it's really just meeting milestones as we go.
"Our line around Kane, at the moment, is still it's unlikely that he will be available, but we certainly don't want to rule out a person of his class and calibre, and the things he brings to this team, too early in case there is that chance still."
Stead said he would consider taking Williamson to the World Cup in a mentoring role to the team's younger players should his injury not recover in time as the Kiwis look to go one step better than their runners-up finish behind England in a thrilling final at Lord's in 2019.
Williamson captained New Zealand in that memorable Super Over decider, but it will be a much different Kiwis' outfit this time around following a recent spate of retirements and contract decisions.
The likes of Ross Taylor, Martin Guptill and Trent Boult have either retired from cricket or no longer hold a central playing contract with the Kiwis and the make-up of New Zealand's squad for this year's World Cup is sure to include a few fresh faces.
One of those players likely to be in the mix is Mark Chapman, after the 28-year-old impressed with a match-winning century in the fifth and final T20I against Pakistan earlier this month.
That knock helped Chapman earn a place in New Zealand's squad for the ODI component of the Pakistan tour and Stead believes the left-hander is a player more than capable of performing well on the big stage.
"The (T20I) series result itself was fantastic for the team, if you consider the number of players that are at the IPL" Stead said.
"And we were playing a full-strength Pakistan team - a team that made the T20 (World Cup) final. So, to get a two-all result against them and play the way we did, especially in the last T20 game, was fantastic.
"The Mark Chapman-James Neesham partnership was really, really significant. Obviously, it wasn't the best of starts with the bat, but the composure the two of them showed in that situation was brilliant.
"It was not just one knock about Mark Chapman why he was added to the ODI squad, but there is a lot of competition for places and it's not so much about the competition, but it's how we keep building towards the World Cup. And Mark Chapman is one guy who is in our thoughts around that."