He added: "If … you hear me say that I want to go to New York, then you can believe it."
Williams holds a player option for the 2012-13 campaign with Utah worth $17.9 million.
He discussed the media circus about his future with the Jazz on Friday, stating that uncertainty surrounding a Collective Bargaining Agreement that will expire June 30 is the main factor affecting his decision to remain in Utah.
"Until I see what that's like, I can't even think about it," Williams said. "I don't want to get into one of those things where everybody's guessing what I'm going to do. I'd rather just leave it at that. You can guess if you want to, but you're not going to know from me."
Williams then used stronger words Sunday, saying that he plans to follow the path of Miami's LeBron James, who refused to answer questions about which team he would join last summer until he finally made a decision.
"I'm not going to answer any questions about it until it's that time," Williams said. "If I say, 'I'm going to opt out after the [2010-11] season concludes next year' I decide what I'm going to do then I'll say it. I haven't decided what I'm going to do."
Williams said it was no coincidence that Sunday's All-Star game was often a well-executed, well-played performance.
With San Antonio's Gregg Popovich and Boston's Doc Rivers coaching, high-percentage shots were displayed more than normal for an exhibition game, and passing was at a premium.
"We were playing hard," Williams said. "We wanted to win."
Los Angeles Clippers rookie Blake Griffin dominated All-Star weekend, participating in three events and enjoying a loud "We want Blake" chant from Sunday's crowd at Staples Center.
Looking slightly worn down, he was held to just eight points and five rebounds during the game. But his first-ever superstar contest left a lasting impression
"I think the things that you remember the most are the time you spend with the other guys around you that are going through the same thing as you," Griffin said.