The 37-year-old forward, who helped Carolina reach the Eastern Conference Final last season and is a three-time Stanley Cup champion, has yet to commit to returning for a 19th NHL season. The Hurricanes open training camp Sept. 12.
"I think he's getting pretty close to making a decision, I know that," Brind'Amour said. "I would expect to hear something, for sure, if not this week, it's coming up quick. Obviously, we have to know."
Williams had 53 points (23 goals, 30 points) in 82 games last season, his first as Carolina captain, and had seven points (four goals, three assists) in 15 Stanley Cup Playoff games. In a text message to the newspaper Wednesday, he said he had "nothing to report."
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Williams became an unrestricted free agent July 1 after the two-year, $9 million contract he signed with the Hurricanes on July 1, 2017, expired. He said at the 2019 NHL Awards in Las Vegas on June 18 that he was in no hurry to decide whether to keep playing.
"I'm going to take my time and make sure I make the right one, right?" Williams said. "Because if I'm all in, I'm going to be all in. If I'm not quite all there, then I have to reassess the situation. I'm not going to be good if I'm 85 percent all in. I've got to be all in. That's the only thing that's fair to me, fair to the teammates, fair to everybody."
Among the factors hinging on Williams' decision from Carolina's point of view is who might succeed him as captain if he does retire.
Brind'Amour said Williams has been spending the offseason consulting with former players on the pros and cons of retirement.
"What I do know is he's talked to a lot of people," Brind'Amour said. "We've talked about it. He's talked to a lot of other people who have recently stopped playing to get their thoughts. He's definitely taking the time because he wants to make the right decision. But we're getting into crunch time here."
Williams has 786 points (312 goals, 474 points) in 1,244 games with the Philadelphia Flyers, Hurricanes, Los Angeles Kings and Washington Capitals, along with 101 points (40 goals, 61 assists) in 155 playoff games. He won the Stanley Cup with the Hurricanes in 2006 and the Kings in 2012 and 2014.