Williams has not played since sustaining an ankle injury during the Rugby World Cup in Japan.
Saracens director of rugby Mark McCall expected the Scarlets-bound British and Irish Lion to return against the Azzurri on 2 February (AEDT).
New Wales head coach Wayne Pivac says Williams will not feature at the Principality Stadium, but hopes he will make his comeback in a blockbuster clash against Ireland in Dublin a week later.
"Liam is on for round two of the competition, he won't make the first game." said Pivac.
Pivac had more positive news of 18-year-old wing Rees-Zammit, who limped out of Gloucester's European Champions Cup defeat to Toulouse last Sunday with an ankle knock but could make his debut when Wales start the defence of their title.
"Louis picked up a bit of a bump last week, he's worked well with the medical team and he'll hopefully be training this morning, doing some running with the boys," Pivac said at the Six Nations launch on Wednesday.
"He'll go back to his club this weekend and then we'll get him back next week."
Wales captain Alun Wyn Jones says the 2019 Grand Slam winners will need time to adjust in a new era under Pivac, who replaced the long-serving Warren Gatland after the World Cup.
The lock said: "It is going to be a bumpy road and we cannot shy away from that. There has been a lot of change and, to a point, we have to cut ties with that.
"But if you continue to look over your shoulder, you will slow yourself down. If we are going to evolve, there are a few more things to adapt to, and that is what you want to do.
"I was asked earlier about desire, and why you keep going, and I just remember why I started. I want to play rugby and I want to be involved with Wales.
"It is Wayne's world now and I am looking forward to what is to come."