Laine, acquired from the Winnipeg Jets on Saturday as part of a blockbuster trade, is playing out the final year of his current contract and will be a restricted free agent this summer. The Blue Jackets hold his rights through the 2022-23 season.
Kekalainen indicated he wants Laine in Columbus for the long haul.
"We're going to try to build a long-term relationship with him," Kekalainen told Sportsnet's Chris Johnston.
With Winnipeg retaining a portion of Laine's salary, the Finnish sniper carries a cap hit of only $5 million for Columbus this season. However, as one of the game's most prolific goal-scorers at 22, he'll certainly require a substantial raise - especially on a long-term deal.
Columbus projects to have over $25 million in cap space this summer, according to CapFriendly, with veterans Nick Foligno, David Savard, and the injured Brandon Dubinsky coming off the books after this season.
Laine's averaged 38 goals per 82 games since entering the league in 2016-17.