Milstein previously denied reports that Panarin provided the Blue Jackets a list of teams he would negotiate a long-term contract with to help facilitate a trade.
"If it was something we'd done (as an organization), I'd try to talk to [Artemi] and go about it in a different way here," Blue Jackets captain Nick Foligno told The Athletic this month. "But there's only so much we can do as players. It's his decision; I respect that. I don't have to agree with it, but I respect it.
"[He] knows how we feel about the city. There's no sell job here. He's seen it. He got to live here for a year, and a successful year too. There's been an embrace for him from staff and fans and management and players. If he doesn't know how we feel about him by now, I don't think he ever will."
Reports have said Panarin is hesitant about living and playing in Columbus.
"I don't want to speak for [him], but it's not like he hates [Columbus]," Foligno said. "I don't want it to sound like he's ever said, 'Oh, I don't like it here,' because he does like it here.
"That's why all of this kind of blindsided me. If you would have asked me when we broke for the summer, I would have said, 'Yeah, he's re-signing, no problem.' But maybe he got back and thought about it and thought about eight years in a city like Columbus.
"If you don't have a family and you don't have that in your plans, then yeah, I could see how it's a little different. Whereas a guy like me or a lot of other guys, we have kids and we've all raised families, and I don't think there's a better place in the country than Columbus to raise a family."
The Blue Jackets acquired Panarin in a trade from the Blackhawks on June 23, 2017. He had 82 points (27 goals, 55 assists) in 81 games last season, his third in the NHL. He had 151 points (61 goals, 90 assists) in two seasons with Chicago, winning the Calder Trophy as NHL rookie of the year in 2015-16.
"You just hope that he wants to win," Foligno said. "If you look around the League, there's only so many teams that have a window to win, and I feel like we're one of them. That's something you hope will change his mind.
"He has an opportunity to be a really good player on a really good team and have a chance to win a championship one day. He's in a position to succeed with our club. That should be a driving force as much as anything for him wanting to stay."