Werenski's 65 goals since entering the NHL in 2016-17 are tied with Alex Pietrangelo, Roman Josi and Victor Hedman for third among defensemen, behind Brent Burns (76) and Dougie Hamilton (72). Of those six players, Werenski has played the fewest games (335).
Jones on Wednesday signed an eight-year, $76 million contract extension ($9.5 million AAV) with the Blackhawks that begins next season.
"I have so much respect for him and he's one of my best friends in hockey, I wish him nothing but the best," Werenski said. "But for me, it's a time now where I can show people what I can do on my own and be the hockey player I can be."
The 24-year-old could be part of the discussion to be the next Columbus captain. Forward Nick Foligno, who was captain since the 2015-16 season, was traded to the Toronto Maple Leafs on April 11.
"I haven't thought about it too much," Werenski said. "We have Boone [Jenner], we have 'Gus' (Gustav Nyquist), we have [Jakub] Voracek now, we have 'Bjorky' (Oliver Bjorkstrand). For me, leadership, there's a hundred different ways you can lead. I'm not the most vocal guy in the room, I still won't be the most vocal guy in the room. For me, it's just leading on the ice and how I play and how hard we work in practice, things like that. Not shy by any means, but I'm not a guy that's going to come in between periods and try and get the guys going. More so how I play on the ice.
"We don't have a captain, not sure what they're going to do, but there's definitely options for them with the guys we have in the room."