"It doesn't bother me," Tavares told the Toronto Star. "I think management understands that role, the importance of that role, the history behind it, everything that surrounds it and what it means to be the captain of the Maple Leafs.
"It's obviously a special honor. In my opinion, it's the right thing to do to take their time. Everyone has to trust that when the time is right, they'll have the right person.
"Whoever it is, there are a lot of great people in the locker room. Everyone will support whoever it is 100 percent."
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Matthews, who turns 21 on Sept. 17, was thought to be the captain in waiting until Tavares signed as a free agent this offseason. Tavares was New York Islanders captain for five seasons.
"I don't think it matters in the sense that it's not going to change the way either of us go about our business, how we are in the locker room, how we treat our teammates and handle everyday life," Matthews told the newspaper. "But obviously the captain plays a big part of the team.
"I think the way that [general manager Kyle Dubas] is handling it is smart, being patient."