"This is going to be a question that we're probably going to have to deal with every day until he does get the green light to go," Kidd said Saturday.
"But we're not rushing him. So if we have to start the season with him still trying to get better, I think we all feel comfortable, but we would feel a little bit more comfortable if he was starting."
Williams, on Sunday, said there was no definitive timetable for his return.
He felt Kidd's comment was overblown by the media.
"I'm not going to respond to anything about yesterday, about this stupidness," Williams said. "That's just how somebody worded a question, and you guys just write it the way you want to, so I'm not going to respond to that."
Kidd, asked after Saturday night's 99-88 preseason loss to the Pistons about Williams possibly being out the first regular-season game and how it would change the mindset of the team in its next five preseason games, said, "I didn't know he was out so ... "
Kidd later added: "I don't go on ifs ... right now we are playing with the guys that are dressed, and he is a day by day situation. If he is ready to go, he will play. We will just take it one day at a time. We got to focus on Sunday."
Williams sprained his right ankle during an offseason workout in Utah.
The point guard participated in shooting drills before Saturday night's game.
Williams had told ESPNNewYork.com on Thursday that he would miss at least the team's next three preseason games due to the injury. He also missed the preseason opener in Washington.
Williams has reiterated that his goal is to play in the team's regular-season opener on Oct. 30 in Cleveland and has felt confident that would happen.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.