In 47 games, total, last season, Gaborik collected 12 goals and 15 assists for 27 points.
"We want to get more familiar with him, get to know him better," Blue Jackets GM Jarmo Kekalainen told the Dispatch. "Sure, we're thinking about it already, but we're going to let it go into the season, hope to see him score a lot of goals for us and then talk about getting him extended."
Gaborik is entering the final year of a five-year, $37.5 million contract. He'll likely command a long-term deal, though his next salary will be determined by his performance on the ice.
Last week, the Blue Jackets signed right wing Nathan Horton to a seven-year contract, and though he'll be out of action until December recovering from shoulder surgery, having him and Gaborik on the right side is an excellent one-two punch.
Gaborik has played in 769 career NHL regular-season games with the Minnesota Wild, Rangers and Blue Jackets, and has accumulated 336 goals and 338 assists for 674 points.
The three-time All-Star was originally drafted third-overall by the Wild in the 2000 NHL Entry Draft.