Like Duchene, neither Bobrovsky nor Panarin has discussed a contract with the Blue Jackets.
Panarin, who was not available to the media Wednesday, said in February he wants to become a free agent and that he could re-sign with Columbus, but that he wanted to see if there were better options. The 27-year-old had 11 points (five goals, six assists) after leading Columbus with 87 points (28 goals, 59 assists) this season, his second with the Blue Jackets.
In January, Bobrovsky declined to comment on a report that he would to waive his no-move clause ahead of the NHL Trade Deadline. He said Wednesday his mind isn't made up to leave.
"It's too early to answer still," he said. "I will think. I will weigh in all the opportunities what we have on the table and then we'll decide."
Bobrovsky was 37-24-1 with a 2.58 goals-against average and .913 save percentage this season, his seventh with the Blue Jackets. He was 6-4 with a 3.14 GAA and .925 save percentage in the playoffs.
Bobrovsky, who will be 31 at the start of next season, said reports of a fractured relationship with management are not true.
"No, I don't feel that way," he said. "There were some ups and downs as always in that process, but we say thank you to each other and it's good."
Duchene had 12 points (four goals, eight assists) in 23 regular-season games with Columbus and was second to Panarin on the Blue Jackets in the playoffs with 10 points (five goals, five assists) in 10 games.
"I've really enjoyed my time here and we will definitely be talking to Jarmo and the Blue Jackets and seeing what's in store," Duchene said. "I'm so happy to be a Blue Jacket. I'm very grateful to be here. Obviously, it will be a great thing if it can continue. We'll see what happens."