New Zealand give Williamson two weeks to prove World Cup fitness
The batsman tore the cruciate ligaments in his right knee playing for Gujarat Titans in the Indian Premier League in April.
The 33-year-old has recovered well and is batting in the nets, with a place in New Zealand's 15-man squad now in sight.
"We've got about two weeks from now until we name that side," Stead told New Zealand media.
"We're going to give him every chance to use that full amount of time. He's in full rehab mode, he's back batting in the nets again, which is great to see.
"He's progressing really well, but there's a lot of work for him still to do to make sure he gets where we need him to be."
Williamson has scored more than 6,500 runs in one-day international cricket and led New Zealand in their nail-biting defeat to England in the 2019 World Cup final.
New Zealand play England in their opening game of the World Cup in Ahmedabad on October 5.
As part of his recovery bid, Williamson is with the squad on their white-ball tour of England.
"Of course we want him at the World Cup, but there is that bigger picture that we want Kane Williamson fit for the rest of his career," added Stead.
"There will be honest conversations that Kane and I will have around exactly where he is at."
All-rounder James Neesham has withdrawn from the Twenty 20 squad for the series against England, which starts Wednesday, to return home ahead of the birth of his first child.