While Kekalainen declined to comment following the meeting, Panarin's agent, Dan Milstein, said it was a "good conversation," but that there was "no contract progress at this time," according to The Athletic's Aaron Portzline.
It was reported back in June that Panarin wasn't ready to consider signing a contract extension with the Blue Jackets, and that Kekalainen was therefore testing the market for him.
The 26-year-old Panarin has one year left on his current two-year, $12-million contract, after which he'll become an unrestricted free agent.
He's coming off his first season with Columbus following a trade that sent Brandon Saad to the Chicago Blackhawks in return. Panarin finished 2017-18 with 27 goals and a career-high 82 points in 81 games.