He is nominated for the Vezina Trophy, given out every year to the NHL's top goaltender, and that has already driven his price up.
In fact, Blue Jackets GM Jarmo Kekalainen is handling negotiations as if he's already won the award.
"I (told his agent), 'Let's just proceed as if he's already won it," Kekalainen told the Dispatch. "Let's take that out of the equation. Let's assume he's won it, and move forward from there."
Bobrovsky's agent, Paul Theofanous, hasn't comment on contract talks, and is believed to be looking to hit a home run for his client, as there is interest from clubs in the KHL.
"His representation is doing what they feel is best; I don't blame them," Kekalainen said. "We're doing what we think is best. I'm not discouraged at all. This is part of the process that both sides have to go through to get a deal done.
"But it's something we'd like to work at, get settled and put behind us."