"We've had some good conversations with his agent, and we're optimistic," Kekalainen told the Columbus Dispatch. "Now we have to focus on the draft, too. That's very important. But we can manage. We're working on it."
Bobrovsky, 24, is scheduled to become a restricted free agent on July 5 if he does not come to terms on a new agreement with the team.
The Blue Jackets are battling with St. Petersburg SKA of the KHL, who pitched an offer to Bobrovsky this week that's believed to be worth $10 million per season.
While Kekalainen is willing to match any offer sheet Bobrovsky were to sign in the NHL, should be become available as an RFA on July 5, dealing with the KHL is an entirely different matter.
"We can't compete with the KHL," he said. "They have different budgets and different rules. We're going to operate under the structure and the contracts that have been signed in this league.
"Nobody wants to lose the Vezina-winning goaltender. That would be foolish to say. Obviously, we want him back, but I've said it before: We need players who want to play for the Columbus Blue Jackets. That's our main focus; that's all we can worry about."
Meanwhile, the Blue Jackets are also trying to lock up center Artem Anisimov, who can also become an RFA next month.
Anisimov, 25, is wrapping up a two-year deal signed in 2011, with an annual salary cap hit of $1.875 million.
"We're pretty close with Anisimov, and again, we're optimistic that we'll get a deal done sooner rather than later," Kekalainen told the Blue Jackets' website. "We've done all of our qualifying offers and all that - those are going out, but we want to respect the process so we communicate with the players. I'm optimistic (Anisimov) will get done here shortly."