The 27-year-old center is entering the final season of a five-year contract he signed with the Colorado Avalanche in 2013. He is eligible to sign a contract extension, but, like Karlsson and Stone, can become an unrestricted free agent July 1, 2019.
"The picture will become clearer for me as it goes," Duchene said during the NHL Player Media Tour on Friday.
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Karlsson, Ottawa's captain, is entering the final season of a seven-year contract he signed June 19, 2012, and has long been rumored to be traded and could be moved before the season begins.
Stone signed a one-year, $7.35 million contract Aug. 3. He had 62 points, including an NHL career-high 42 assists, in 58 games last season.
"Those are the things I want to sit back and watch," Duchene said. "The nice thing is is I'm kind of the last domino in that sense. Those are things I want to see.
"Erik, that's a little bit different situation, but with [Mark], that's a guy I'd love to move forward with as a teammate. Him doing a one-year deal, it's a little bit different and makes you think a little bit, but I want to see what he's saying and we'll talk through it. Having talked about it, we both really like it in Ottawa and we both want it to work, so that's the biggest thing."