Williams told New Zealand radio Wednesday that he and Woods remain close friends and there is no possibility their working relationship is about to end.
"I'm sure if there was going to be some sort of parting of the ways, I'd be the first to know," he said. "From my point of view, I don't see any chance of that happening."
Williams said Woods had no plans to change his key personnel, though he has struggled to regain form after taking a break from the PGA Tour amid revelations of marital infidelities.
"People speculate. He's not playing well and his results aren't what we're used to," Williams, of New Zealand, said. "Tiger and I are very good friends and we've been through a tough time. There's no question about that.
"I'm fully supportive of the guy and he's been great through this whole situation with me."
Woods consulted with swing coach Sean Foley at the PGA, but it's unclear whether he will work with him full time.
"He hasn't decided if that's the coach who's going to be with him, but I really like what this new guy had to say and what his theories are," Williams said. "If Tiger decides to stick with Sean, I believe he'll get better. It might take a little while."
Woods finished 28th at last week's PGA Championship in Wisconsin, a week after posting the worst 72-hole total of his career — 18 over par — at the Bridgestone Invitational event in Ohio.
Williams said nobody should rush to the conclusion Woods was losing his ability or his aura.
"At the end of the day, Tiger Woods is Tiger Woods," Williams said. "He's won 14 majors and 71 PGA Tour events. Regardless of what's gone on, you can't take that away from the guy.
"Tiger knows how to win and people know that he knows how to win. When he gets back in the situation where he's playing well again and he's in contention to win, he'll get the job done."
"It's one of the biggest events in the world and anybody that's played in it before always has the desire to play in it again," Williams said. "We've got a couple more weeks to show him (Pavin) that he's playing better."