The 27-year-old Panarin, along with goalie Sergei Bobrovsky, can become an unrestricted free agent on July 1. Panarin has 53 points (19 goals, 34 assists) in 46 games to lead the Blue Jackets this season.
Panarin and agent Daniel Milstein met this weekend in Miami, according to The Athletic. It was reported in November that Panarin would meet with his agent in January to discuss his future with the Blue Jackets.
"We're going to get some answers and then we're going to have to make decisions," Columbus general manager Jarmo Kekalainen told the Blue Jackets website on Jan. 21. "They're obviously two very talented players, two guys that have been a big part of our success, so that makes it a little bit more intriguing from the outside and people are curious to see how all of this is going to play out.
"But we will do what we need to do, do our best to convince them that they'd like to be part of our future for a long time as a Blue Jacket in Columbus, and if that doesn't happen, then we're going to have to make decisions. ... and if we have to make hard decisions, we'll make them."
Panarin is in the final season of a two-year contract he signed with the Chicago Blackhawks on Dec. 28, 2016. He has been eligible to sign a contract extension with the Blue Jackets since July 1, 2018; however, he said he would not have contract discussions during the season after the two sides failed to reach an agreement prior to training camp in September.
Columbus (28-17-3) is third in the Metropolitan Division and returned to practice Sunday following its mandatory five-day break and the 2019 Honda NHL All-Star Weekend in San Jose.
"I feel great about our core, and it's only going to get better," Kekalainen said. "I've said it many times, we had 108 points in the regular season before Artemi Panarin arrived. That's not to slight Artemi at all. We love him, he's a great player and he makes our team better, and if for some reason he doesn't want to stay here we'll move along and we'll be a strong team in the future as well. We hope he stays. We'll do our best to convince him and we'll see what happens."