On Sunday, midfielder Williams was rumoured to be heading home from Japan with a calf injury, but those rumours were quickly shut down by the All Blacks.
Former rugby reporter Hamish McKay told Radio Sport Williams would be replaced by Manawatu Turbos midfielder Ngani Laumape.
But sources told Newshub that Laumape had not received a call from All Blacks management to join the squad.
All Blacks assistant coach Ian Foster said Williams was carrying an injury, but the team was doing a good job managing it.
"Is he going home?" said Foster. "No.
"Is he available for selection based on his progression last week? Then I think the answer is yes.
"He's trained really well and got through it. I think we said last week we had a progression plan for a number of the guys who brought niggles into the week and overall came through pretty good."
Asked whether New Zealand were considering any call-ups, Foster added: "I've just answered that question - there's no people needed."
Laumape was considered unlucky to have missed out on the 31-man World Cup squad, but has since put two impressive performances together for Manawatu.